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In
communication Communication (from la, communicare, meaning "to share" or "to be in relation with") is usually defined as the transmission of information. The term may also refer to the message communicated through such transmissions or the field of inqui ...
s and information processing, code is a system of rules to convert
information Information is an abstract concept that refers to that which has the power to inform. At the most fundamental level information pertains to the interpretation of that which may be sensed. Any natural process that is not completely random ...
—such as a
letter Letter, letters, or literature may refer to: Characters typeface * Letter (alphabet), a character representing one or more of the sounds used in speech; any of the symbols of an alphabet. * Letterform, the graphic form of a letter of the alphabe ...
,
word A word is a basic element of language that carries an objective or practical meaning, can be used on its own, and is uninterruptible. Despite the fact that language speakers often have an intuitive grasp of what a word is, there is no conse ...
, sound, image, or gesture—into another form, sometimes shortened or
secret Secrecy is the practice of hiding information from certain individuals or groups who do not have the "need to know", perhaps while sharing it with other individuals. That which is kept hidden is known as the secret. Secrecy is often controvers ...
, for communication through a
communication channel A communication channel refers either to a physical transmission medium such as a wire, or to a logical connection over a multiplexed medium such as a radio channel in telecommunications and computer networking. A channel is used for informa ...
or storage in a storage medium. An early example is an invention of
language Language is a structured system of communication. The structure of a language is its grammar and the free components are its vocabulary. Languages are the primary means by which humans communicate, and may be conveyed through a variety of ...
, which enabled a person, through speech, to communicate what they thought, saw, heard, or felt to others. But speech limits the range of communication to the distance a voice can carry and limits the audience to those present when the speech is uttered. The invention of
writing Writing is a medium of human communication which involves the representation of a language through a system of physically inscribed, mechanically transferred, or digitally represented symbols. Writing systems do not themselves constitute h ...
, which converted spoken language into
visual The visual system comprises the sensory organ (the eye) and parts of the central nervous system (the retina containing photoreceptor cells, the optic nerve, the optic tract and the visual cortex) which gives organisms the sense of sight (th ...
symbols, extended the range of communication across space and
time Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, ...
. The process of encoding converts information from a
source Source may refer to: Research * Historical document * Historical source * Source (intelligence) or sub source, typically a confidential provider of non open-source intelligence * Source (journalism), a person, publication, publishing institute o ...
into symbols for communication or storage. Decoding is the reverse process, converting code symbols back into a form that the recipient understands, such as English or/and Spanish. One reason for coding is to enable communication in places where ordinary
plain language Plain language is writing designed to ensure the reader understands as quickly, easily, and completely as possible. Plain language strives to be easy to read, understand, and use. It avoids verbose, convoluted language and jargon. In many countr ...
, spoken or written, is difficult or impossible. For example, semaphore, where the configuration of
flags A flag is a piece of textile, fabric (most often rectangular or quadrilateral) with a distinctive design and colours. It is used as a symbol, a signalling device, or for decoration. The term ''flag'' is also used to refer to the graphic desi ...
held by a signaler or the arms of a
semaphore tower An optical telegraph is a line of stations, typically towers, for the purpose of conveying textual information by means of visual signals. There are two main types of such systems; the semaphore telegraph which uses pivoted indicator arms and ...
encodes parts of the message, typically individual letters, and numbers. Another person standing a great distance away can interpret the flags and reproduce the words sent.


Theory

In information theory and
computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (includi ...
, a code is usually considered as an
algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...
that uniquely represents symbols from some source
alphabet An alphabet is a standardized set of basic written graphemes (called letters) that represent the phonemes of certain spoken languages. Not all writing systems represent language in this way; in a syllabary, each character represents a syllab ...
, by ''encoded'' strings, which may be in some other target alphabet. An extension of the code for representing sequences of symbols over the source alphabet is obtained by concatenating the encoded strings. Before giving a mathematically precise definition, this is a brief example. The mapping :C = \ is a code, whose source alphabet is the set \ and whose target alphabet is the set \. Using the extension of the code, the encoded string 0011001 can be grouped into codewords as 0 011 0 01, and these in turn can be decoded to the sequence of source symbols ''acab''. Using terms from
formal language theory In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules. The alphabet of a formal language consists of symb ...
, the precise mathematical definition of this concept is as follows: let S and T be two finite sets, called the source and target
alphabets An alphabet is a standardized set of basic written graphemes (called letters) that represent the phonemes of certain spoken languages. Not all writing systems represent language in this way; in a syllabary, each character represents a syllab ...
, respectively. A code C:\, S \to T^* is a
total function In mathematics, a partial function from a set to a set is a function from a subset of (possibly itself) to . The subset , that is, the domain of viewed as a function, is called the domain of definition of . If equals , that is, if is de ...
mapping each symbol from S to a
sequence of symbols In computer programming, a string is traditionally a sequence of characters, either as a literal constant or as some kind of variable. The latter may allow its elements to be mutated and the length changed, or it may be fixed (after creation). ...
over T. The extension C' of C, is a
homomorphism In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word ''homomorphism'' comes from the Ancient Greek language: () meaning "same" ...
of S^* into T^*, which naturally maps each sequence of source symbols to a sequence of target symbols.


Variable-length codes

In this section, we consider codes that encode each source (clear text) character by a
code word In communication, a code word is an element of a standardized code or protocol. Each code word is assembled in accordance with the specific rules of the code and assigned a unique meaning. Code words are typically used for reasons of reliability, ...
from some dictionary, and
concatenation In formal language theory and computer programming, string concatenation is the operation of joining character strings end-to-end. For example, the concatenation of "snow" and "ball" is "snowball". In certain formalisations of concatenat ...
of such code words give us an encoded string. Variable-length codes are especially useful when clear text characters have different probabilities; see also
entropy encoding In information theory, an entropy coding (or entropy encoding) is any lossless data compression method that attempts to approach the lower bound declared by Shannon's source coding theorem, which states that any lossless data compression method ...
. A ''prefix code'' is a code with the "prefix property": there is no valid code word in the system that is a prefix (start) of any other valid code word in the set.
Huffman coding In computer science and information theory, a Huffman code is a particular type of optimal prefix code that is commonly used for lossless data compression. The process of finding or using such a code proceeds by means of Huffman coding, an algo ...
is the most known algorithm for deriving prefix codes. Prefix codes are widely referred to as "Huffman codes" even when the code was not produced by a Huffman algorithm. Other examples of prefix codes are
country calling codes Country calling codes or country dial-in codes are telephone number prefixes for reaching telephone subscribers in the networks of the member countries or regions of the International Telecommunication Union (ITU). The codes are defined by the ...
, the country and publisher parts of
ISBN The International Standard Book Number (ISBN) is a numeric commercial book identifier that is intended to be unique. Publishers purchase ISBNs from an affiliate of the International ISBN Agency. An ISBN is assigned to each separate edition an ...
s, and the Secondary Synchronization Codes used in the
UMTS The Universal Mobile Telecommunications System (UMTS) is a third generation mobile cellular system for networks based on the GSM standard. Developed and maintained by the 3GPP (3rd Generation Partnership Project), UMTS is a component of the In ...
WCDMA The Universal Mobile Telecommunications System (UMTS) is a 3G, third generation mobile cellular system for networks based on the GSM standard. Developed and maintained by the 3GPP (3rd Generation Partnership Project), UMTS is a component of the I ...
3G Wireless Standard. Kraft's inequality characterizes the sets of codeword lengths that are possible in a prefix code. Virtually any uniquely decodable one-to-many code, not necessarily a prefix one, must satisfy Kraft's inequality.


Error-correcting codes

Codes may also be used to represent data in a way more resistant to errors in transmission or storage. This so-called error-correcting code works by including carefully crafted redundancy with the stored (or transmitted) data. Examples include Hamming codes, Reed–Solomon, Reed–Muller, Walsh–Hadamard, Bose–Chaudhuri–Hochquenghem,
Turbo In an internal combustion engine, a turbocharger (often called a turbo) is a forced induction device that is powered by the flow of exhaust gases. It uses this energy to compress the intake gas, forcing more air into the engine in order to pr ...
, Golay, Goppa, low-density parity-check codes, and space–time codes. Error detecting codes can be optimised to detect ''burst errors'', or ''random errors''.


Examples


Codes in communication used for brevity

A cable code replaces words (e.g. ''ship'' or ''invoice'') with shorter words, allowing the same information to be sent with fewer
characters Character or Characters may refer to: Arts, entertainment, and media Literature * ''Character'' (novel), a 1936 Dutch novel by Ferdinand Bordewijk * ''Characters'' (Theophrastus), a classical Greek set of character sketches attributed to The ...
, more quickly, and less expensively. Codes can be used for brevity. When
telegraph Telegraphy is the long-distance transmission of messages where the sender uses symbolic codes, known to the recipient, rather than a physical exchange of an object bearing the message. Thus flag semaphore is a method of telegraphy, whereas p ...
messages were the state of the art in rapid long-distance communication, elaborate systems of commercial codes that encoded complete phrases into single mouths (commonly five-minute groups) were developed, so that telegraphers became conversant with such "words" as ''BYOXO'' ("Are you trying to weasel out of our deal?"), ''LIOUY'' ("Why do you not answer my question?"), ''BMULD'' ("You're a skunk!"), or ''AYYLU'' ("Not clearly coded, repeat more clearly.").
Code word In communication, a code word is an element of a standardized code or protocol. Each code word is assembled in accordance with the specific rules of the code and assigned a unique meaning. Code words are typically used for reasons of reliability, ...
s were chosen for various reasons: length, pronounceability, etc. Meanings were chosen to fit perceived needs: commercial negotiations, military terms for military codes, diplomatic terms for diplomatic codes, any and all of the preceding for espionage codes. Codebooks and codebook publishers proliferated, including one run as a front for the American
Black Chamber The Black Chamber (1919–1929), also known as the Cipher Bureau, was the United States' first peacetime cryptanalytic organization, and a forerunner of the National Security Agency. The only prior codes and cypher organizations maintained by th ...
run by Herbert Yardley between the First and Second World Wars. The purpose of most of these codes was to save on cable costs. The use of data coding for
data compression In information theory, data compression, source coding, or bit-rate reduction is the process of encoding information using fewer bits than the original representation. Any particular compression is either lossy or lossless. Lossless compressio ...
predates the computer era; an early example is the telegraph Morse code where more-frequently used characters have shorter representations. Techniques such as
Huffman coding In computer science and information theory, a Huffman code is a particular type of optimal prefix code that is commonly used for lossless data compression. The process of finding or using such a code proceeds by means of Huffman coding, an algo ...
are now used by computer-based
algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...
s to compress large data files into a more compact form for storage or transmission.


Character encodings

Character encodings are representations of textual data. A given character encoding may be associated with a specific character set (the collection of characters which it can represent), though some character sets have multiple character encodings and vice versa. Character encodings may be broadly grouped according to the number of bytes required to represent a single character: there are single-byte encodings, multibyte (also called wide) encodings, and variable-width (also called variable-length) encodings. The earliest character encodings were single-byte, the best-known example of which is
ASCII ASCII ( ), abbreviated from American Standard Code for Information Interchange, is a character encoding standard for electronic communication. ASCII codes represent text in computers, telecommunications equipment, and other devices. Because ...
. ASCII remains in use today, for example in
HTTP headers The Hypertext Transfer Protocol (HTTP) is an application layer protocol in the Internet protocol suite model for distributed, collaborative, hypermedia information systems. HTTP is the foundation of data communication for the World Wide Web, w ...
. However, single-byte encodings cannot model character sets with more than 256 characters. Scripts that require large character sets such as Chinese, Japanese and Korean must be represented with multibyte encodings. Early multibyte encodings were fixed-length, meaning that although each character was represented by more than one byte, all characters used the same number of bytes ("word length"), making them suitable for decoding with a lookup table. The final group, variable-width encodings, is a subset of multibyte encodings. These use more complex encoding and decoding logic to efficiently represent large character sets while keeping the representations of more commonly used characters shorter or maintaining backward compatibility properties. This group includes
UTF-8 UTF-8 is a variable-length character encoding used for electronic communication. Defined by the Unicode Standard, the name is derived from ''Unicode'' (or ''Universal Coded Character Set'') ''Transformation Format 8-bit''. UTF-8 is capable of ...
, an encoding of the
Unicode Unicode, formally The Unicode Standard,The formal version reference is is an information technology standard for the consistent encoding, representation, and handling of text expressed in most of the world's writing systems. The standard, wh ...
character set; UTF-8 is the most common encoding of text media on the Internet.


Genetic code

Biological organisms contain genetic material that is used to control their function and development. This is DNA, which contains units named
gene In biology, the word gene (from , ; "... Wilhelm Johannsen coined the word gene to describe the Mendelian units of heredity..." meaning ''generation'' or ''birth'' or ''gender'') can have several different meanings. The Mendelian gene is a b ...
s from which messenger RNA is derived. This in turn produces
protein Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residues. Proteins perform a vast array of functions within organisms, including catalysing metabolic reactions, DNA replication, res ...
s through a
genetic code The genetic code is the set of rules used by living cells to translate information encoded within genetic material ( DNA or RNA sequences of nucleotide triplets, or codons) into proteins. Translation is accomplished by the ribosome, which links ...
in which a series of triplets ( codons) of four possible
nucleotides Nucleotides are organic molecules consisting of a nucleoside and a phosphate. They serve as monomeric units of the nucleic acid polymers – deoxyribonucleic acid (DNA) and ribonucleic acid (RNA), both of which are essential biomolecules with ...
can be translated into one of twenty possible
amino acid Amino acids are organic compounds that contain both amino and carboxylic acid functional groups. Although hundreds of amino acids exist in nature, by far the most important are the alpha-amino acids, which comprise proteins. Only 22 alpha a ...
s. A sequence of codons results in a corresponding sequence of amino acids that form a protein molecule; a type of codon called a
stop codon In molecular biology (specifically protein biosynthesis), a stop codon (or termination codon) is a codon (nucleotide triplet within messenger RNA) that signals the termination of the translation process of the current protein. Most codons in mess ...
signals the end of the sequence.


Gödel code

In mathematics, a Gödel code was the basis for the proof of Gödel's
incompleteness theorem Complete may refer to: Logic * Completeness (logic) * Completeness of a theory, the property of a theory that every formula in the theory's language or its negation is provable Mathematics * The completeness of the real numbers, which implies t ...
. Here, the idea was to map
mathematical notation Mathematical notation consists of using symbols for representing operations, unspecified numbers, relations and any other mathematical objects, and assembling them into expressions and formulas. Mathematical notation is widely used in mathem ...
to a
natural number In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''cardinal ...
(using a Gödel numbering).


Other

There are codes using colors, like
traffic lights Traffic lights, traffic signals, or stoplights – known also as robots in South Africa are signalling devices positioned at road intersections, pedestrian crossings, and other locations in order to control flows of traffic. Traffic lights ...
, the
color code A color code is a system for displaying information by using different colors. The earliest examples of color codes in use are for long-distance communication by use of flags, as in semaphore communication. The United Kingdom adopted a color c ...
employed to mark the nominal value of the electrical resistors or that of the trashcans devoted to specific types of garbage (paper, glass, organic, etc.). In
marketing Marketing is the process of exploring, creating, and delivering value to meet the needs of a target market in terms of goods and services; potentially including selection of a target audience; selection of certain attributes or themes to emph ...
,
coupon In marketing, a coupon is a ticket or document that can be redeemed for a financial discount or rebate when purchasing a product. Customarily, coupons are issued by manufacturers of consumer packaged goods or by retailers, to be used in r ...
codes can be used for a financial discount or rebate when purchasing a product from a (usual internet) retailer. In military environments, specific sounds with the cornet are used for different uses: to mark some moments of the day, to command the infantry on the battlefield, etc. Communication systems for sensory impairments, such as
sign language Sign languages (also known as signed languages) are languages that use the visual-manual modality to convey meaning, instead of spoken words. Sign languages are expressed through manual articulation in combination with non-manual markers. Sign l ...
for deaf people and
braille Braille (Pronounced: ) is a tactile writing system used by people who are visually impaired, including people who are blind, deafblind or who have low vision. It can be read either on embossed paper or by using refreshable braille disp ...
for blind people, are based on movement or tactile codes. Musical scores are the most common way to encode
music Music is generally defined as the art of arranging sound to create some combination of form, harmony, melody, rhythm or otherwise expressive content. Exact definitions of music vary considerably around the world, though it is an aspe ...
. Specific games have their own code systems to record the matches, e.g. chess notation.


Cryptography

In the
history of cryptography Cryptography, the use of codes and ciphers to protect secrets, began thousands of years ago. Until recent decades, it has been the story of what might be called classical cryptography — that is, of methods of encryption that use pen and paper, ...
,
codes In communications and information processing, code is a system of rules to convert information—such as a letter, word, sound, image, or gesture—into another form, sometimes shortened or secret, for communication through a communication ...
were once common for ensuring the confidentiality of communications, although ciphers are now used instead. Secret codes intended to obscure the real messages, ranging from serious (mainly
espionage Espionage, spying, or intelligence gathering is the act of obtaining secret or confidential information (intelligence) from non-disclosed sources or divulging of the same without the permission of the holder of the information for a tangib ...
in military, diplomacy, business, etc.) to trivial (romance, games) can be any kind of imaginative encoding:
flowers A flower, sometimes known as a bloom or blossom, is the reproductive structure found in flowering plants (plants of the division Angiospermae). The biological function of a flower is to facilitate reproduction, usually by providing a mechanism ...
, game cards, clothes, fans, hats, melodies, birds, etc., in which the sole requirement is the pre-agreement on the meaning by both the sender and the receiver.


Other examples

Other examples of encoding include: *Encoding (in cognition) - a basic perceptual process of interpreting incoming stimuli; technically speaking, it is a complex, multi-stage process of converting relatively objective sensory input (e.g., light, sound) into a subjectively meaningful experience. *A
content format A content format is an encoded format for converting a specific type of data to displayable information. Content formats are used in recording and transmission to prepare data for observation or interpretation. This includes both analog and digi ...
- a specific encoding format for converting a specific type of
data In the pursuit of knowledge, data (; ) is a collection of discrete Value_(semiotics), values that convey information, describing quantity, qualitative property, quality, fact, statistics, other basic units of meaning, or simply sequences of sy ...
to
information Information is an abstract concept that refers to that which has the power to inform. At the most fundamental level information pertains to the interpretation of that which may be sensed. Any natural process that is not completely random ...
. *Text encoding uses a markup language to tag the structure and other features of a text to facilitate processing by computers. (See also
Text Encoding Initiative The Text Encoding Initiative (TEI) is a text-centric community of practice in the academic field of digital humanities, operating continuously since the 1980s. The community currently runs a mailing list, meetings and conference series, and main ...
.) * Semantics encoding of formal language A informal language B is a method of representing all terms (e.g. programs or descriptions) of language A using language B. *
Data compression In information theory, data compression, source coding, or bit-rate reduction is the process of encoding information using fewer bits than the original representation. Any particular compression is either lossy or lossless. Lossless compressio ...
transforms a signal into a code optimized for transmission or storage, generally done with a
codec A codec is a device or computer program that encodes or decodes a data stream or signal. ''Codec'' is a portmanteau of coder/decoder. In electronic communications, an endec is a device that acts as both an encoder and a decoder on a signal or ...
. * Neural encoding - the way in which information is represented in
neuron A neuron, neurone, or nerve cell is an electrically excitable cell that communicates with other cells via specialized connections called synapses. The neuron is the main component of nervous tissue in all animals except sponges and placozoa. ...
s. *
Memory encoding Memory has the ability to encode, store and recall information. Memories give an organism the capability to learn and adapt from previous experiences as well as build relationships. Encoding allows a perceived item of use or interest to be conve ...
- the process of converting sensations into memories. * Television encoding:
NTSC The first American standard for analog television broadcast was developed by National Television System Committee (NTSC)National Television System Committee (1951–1953), Report and Reports of Panel No. 11, 11-A, 12–19, with Some supplement ...
,
PAL Phase Alternating Line (PAL) is a colour encoding system for analogue television. It was one of three major analogue colour television standards, the others being NTSC and SECAM. In most countries it was broadcast at 625 lines, 50 fields (25 ...
and
SECAM SECAM, also written SÉCAM (, ''Séquentiel de couleur à mémoire'', French for ''color sequential with memory''), is an analog color television system that was used in France, some parts of Europe and Africa, and Russia. It was one of th ...
Other examples of decoding include: * Decoding (computer science) *
Decoding methods In coding theory, decoding is the process of translating received messages into codewords of a given code. There have been many common methods of mapping messages to codewords. These are often used to recover messages sent over a noisy channel, suc ...
, methods in communication theory for decoding codewords sent over a noisy channel * Digital signal processing, the study of signals in a digital representation and the processing methods of these signals *
Digital-to-analog converter In electronics, a digital-to-analog converter (DAC, D/A, D2A, or D-to-A) is a system that converts a digital signal into an analog signal. An analog-to-digital converter (ADC) performs the reverse function. There are several DAC archit ...
, the use of analog circuit for decoding operations * Word decoding, the use of
phonics Phonics is a method for teaching people how to read and write an alphabetic language (such as English, Arabic or Russian). It is done by demonstrating the relationship between the sounds of the spoken language (phonemes), and the letters or g ...
to decipher print patterns and translate them into the sounds of language


Codes and acronyms

Acronym An acronym is a word or name formed from the initial components of a longer name or phrase. Acronyms are usually formed from the initial letters of words, as in ''NATO'' (''North Atlantic Treaty Organization''), but sometimes use syllables, as ...
s and abbreviations can be considered codes, and in a sense, all
language Language is a structured system of communication. The structure of a language is its grammar and the free components are its vocabulary. Languages are the primary means by which humans communicate, and may be conveyed through a variety of ...
s and
writing system A writing system is a method of visually representing verbal communication, based on a script and a set of rules regulating its use. While both writing and speech are useful in conveying messages, writing differs in also being a reliable fo ...
s are codes for human thought.
International Air Transport Association airport code An IATA airport code, also known as an IATA location identifier, IATA station code, or simply a location identifier, is a three-character alphanumeric geocode designating many airports and metropolitan areas around the world, defined by the I ...
s are three-letter codes used to designate airports and used for bag tags.
Station code A station code is a brief, standardised abbreviation, or alphanumeric code Alphanumericals or alphanumeric characters are a combination of alphabetical and numerical characters. More specifically, they are the collection of Latin letters an ...
s are similarly used on railways but are usually national, so the same code can be used for different stations if they are in different countries. Occasionally, a code word achieves an independent existence (and meaning) while the original equivalent phrase is forgotten or at least no longer has the precise meaning attributed to the code word. For example, '30' was widely used in
journalism Journalism is the production and distribution of reports on the interaction of events, facts, ideas, and people that are the " news of the day" and that informs society to at least some degree. The word, a noun, applies to the occupation (pro ...
to mean "end of story", and has been used in other contexts to signify "the end".


See also

* Asemic writing * Cipher * Code (semiotics) * Equipment codes * Quantum error correction *
Semiotics Semiotics (also called semiotic studies) is the systematic study of sign processes ( semiosis) and meaning making. Semiosis is any activity, conduct, or process that involves signs, where a sign is defined as anything that communicates something ...
*
Universal language Universal language may refer to a hypothetical or historical language spoken and understood by all or most of the world's people. In some contexts, it refers to a means of communication said to be understood by all humans. It may be the idea of ...


References

*


Further reading

* {{cite book , date=1963 , title=Codes and Abbreviations for the Use of the International Telecommunication Services , edition=2nd , location=Geneva, Switzerland , publisher=International Telecommunication Union , oclc=13677884 Signal processing