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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 inquir ...
s and
information processing Information processing is the change (processing) of information in any manner detectable by an observation, observer. As such, it is a process that ''describes'' everything that happens (changes) in the universe, from the falling of a rock (a ch ...
, code is a system of rules to convert
information Information is an Abstraction, abstract concept that refers to that which has the power to Communication, inform. At the most fundamental level information pertains to the Interpretation (logic), interpretation of that which may be sensed. ...
—such as a letter,
word A word is a basic element 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, ...
, sound, image, or
gesture A gesture is a form of non-verbal communication or non-vocal communication in which visible bodily actions communicate particular messages, either in place of, or in conjunction with, speech. Gestures include movement of the hands, face, or ot ...
—into another form, sometimes shortened or secret, for communication through a
communication channel A communication channel refers either to a physical transmission medium A transmission medium is a system or substance that can mediate the wave propagation, propagation of signals for the purposes of telecommunication. Signals are typical ...
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 met ...
, which enabled a person, through
speech Speech is a human vocal communication using language. Each language uses Phonetics, phonetic combinations of vowel and consonant sounds that form the sound of its words (that is, all English words sound different from all French words, even if ...
, 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 Epigraphy, inscribed, Printing press, mechanically transferred, or Word processor, digitally represented Symbols (semiot ...
, which converted spoken language into visual
symbol A symbol is a mark, sign, or word that indicates, signifies, or is understood as representing an idea, object, or relationship. Symbols allow people to go beyond what is known or seen by creating linkages between otherwise very different ...
s, extended the range of communication across space and
time Time is the continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past, through the present, into the future. It is a component quantity of various me ...
. 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, spoken or written, is difficult or impossible. For example,
semaphore Semaphore (; ) is the use of an apparatus to create a visual signal transmitted over distance. A semaphore can be performed with devices including: fire, lights, flags, sunlight, and moving arms. Semaphores can be used for telegraphy when arra ...
, where the configuration of flags 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 Information theory is the scientific study of the quantification (science), quantification, computer data storage, storage, and telecommunication, communication of information. The field was originally established by the works of Harry Nyquist a ...
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 Applied science, practical discipli ...
, 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 Computational problem, problems or to perform a computation. Algorithms are used as specificat ...
that uniquely represents
symbols A symbol is a mark, sign, or word that indicates, signifies, or is understood as representing an idea, object, or relationship. Symbols allow people to go beyond what is known or seen by creating linkages between otherwise very different ...
from some source
alphabet An alphabet is a standardized set of basic written graphemes (called letter (alphabet), letters) that represent the phonemes of certain spoken languages. Not all writing systems represent language in this way; in a syllabary, each character ...
, 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, the precise mathematical definition of this concept is as follows: let S and T be two finite sets, called the source and target alphabets, respectively. A code C:\, S \to T^* is a total function mapping each symbol from S to a sequence of symbols over T. The extension C' of C, is a
homomorphism In algebra, a homomorphism is a morphism, structure-preserving map (mathematics), map between two algebraic structures of the same type (such as two group (mathematics), groups, two ring (mathematics), rings, or two vector spaces). The word ''homo ...
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 from some dictionary, and
concatenation In formal language, formal language theory and computer programming, string concatenation is the operation of joining character string (computer science), character strings wikt:end-to-end, end-to-end. For example, the concatenation of "sno ...
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. A ''prefix code'' is a code with the "prefix property": there is no valid code word in the system that is a
prefix A prefix is an affix which is placed before the Word stem, stem of a word. Adding it to the beginning of one word changes it into another word. For example, when the prefix ''un-'' is added to the word ''happy'', it creates the word ''unhappy'' ...
(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 algori ...
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, 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 and ...
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 I ...
WCDMA 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 code In computer science and telecommunication, Hamming codes are a family of linear code, linear error-correcting codes. Hamming codes can detect one-bit and two-bit errors, or correct one-bit errors without detection of uncorrected errors. By contr ...
s, 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 pro ...
, 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, 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 words were chosen for various reasons:
length Length is a measure of distance. In the International System of Quantities, length is a quantity with Dimension (physical quantity), dimension distance. In most Measurement system, systems of measurement a Base unit (measurement), base unit f ...
, 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 the ...
run by
Herbert Yardley Herbert Osborn Yardley (April 13, 1889 – August 7, 1958) was an American cryptologist. He founded and led the cryptographic organization the Black Chamber. Under Yardley, the cryptanalysts of The American Black Chamber broke Japanese diplomatic ...
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 compression, lossy or Lossless com ...
predates the computer era; an early example is the telegraph
Morse code Morse code is a method used in telecommunication to Character encoding, encode Written language, text characters as standardized sequences of two different signal durations, called ''dots'' and ''dashes'', or ''dits'' and ''dahs''. Morse cod ...
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 algori ...
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 Computational problem, problems or to perform a computation. Algorithms are used as specificat ...
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 of ...
. ASCII remains in use today, for example in HTTP headers. 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 Character encoding is the process of assigning numbers to Graphics, graphical character (computing), characters, especially the written characters of Language, human language, allowing them to be ...
, 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, ...
character set; UTF-8 is the most common encoding of text media on the Internet.


Genetic code

Biological Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary i ...
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 inheritance#History, Mendelian units of heredity..." meaning ''generation'' or ''birth'' or ''gender'') can have several different meanin ...
s from which
messenger RNA In molecular biology, messenger ribonucleic acid (mRNA) is a single-stranded molecule of RNA that corresponds to the genetic sequence of a gene, and is read by a ribosome in the process of Protein biosynthesis, synthesizing a protein. mRNA is ...
is derived. This in turn produces
protein Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residue (biochemistry), residues. Proteins perform a vast array of functions within organisms, including Enzyme catalysis, catalysing metabo ...
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 protein Proteins are large biomolecules and macromolecules ...
in which a series of triplets (
codon The genetic code is the set of rules used by living cell (biology), cells to Translation (biology), translate information encoded within genetic material (DNA or RNA sequences of nucleotide triplets, or codons) into proteins. Translation is accom ...
s) of four possible
nucleotides Nucleotides are organic molecules consisting of a nucleoside and a phosphate. They serve as monomer In chemistry, a monomer ( ; ''wikt:mono-, mono-'', "one" + ''wikt:-mer, -mer'', "part") is a molecule that can chemical reaction, react tog ...
can be translated into one of twenty possible
amino acid Amino acids are organic compound In chemistry, organic compounds are generally any chemical compounds that contain carbon-hydrogen or carbon-carbon chemical bond, bonds. Due to carbon's ability to Catenation, catenate (form chains with ot ...
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 Genetic code, codon (nucleotide triplet within messenger RNA) that signals the termination of the translation (biology), translation process of the ...
signals the end of the sequence.


Gödel code

In
mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
, a Gödel code was the basis for the proof of Gödel's incompleteness theorem. Here, the idea was to map mathematical notation 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 n ...
(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 intersection (road), road intersections, pedestrian crossings, and other locations in order to control flows of traf ...
, 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 Flag semaphore, semaphore communication. The United Kingdom a ...
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 empha ...
,
coupon In marketing, a coupon is a ticket or document that can be redeemed for a financial discounts and allowances, discount or rebate (marketing), rebate when purchasing a product (business), product. Customarily, coupons are issued by manufacturers ...
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 The cornet (, ) is a brass instrument similar to the trumpet but distinguished from it by its conical Bore (wind instruments), bore, more compact shape, and mellower tone quality. The most common cornet is a transposing instrument in B, thou ...
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 Blindness, blind, Deafblindness, deafblind or who have low vision. It can be read either on Paper embossing, embossed paper ...
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 The arts, art of arranging sound to create some combination of Musical form, form, harmony, melody, rhythm or otherwise Musical expression, expressive content. Exact definition of music, definitions of mu ...
. 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 were once common for ensuring the confidentiality of communications, although
cipher In cryptography, a cipher (or cypher) is an algorithm for performing encryption or decryption—a series of well-defined steps that can be followed as a procedure. An alternative, less common term is ''encipherment''. To encipher or encode i ...
s 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 Secrecy, secret or Confidentiality, confidential information (Intelligence assessment, intelligence) from non-disclosed sources or divulging of the same without the Consent ...
in military, diplomacy, business, etc.) to trivial (romance, games) can be any kind of imaginative encoding: flowers, 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 Cognition refers to "the mental action or process of acquiring knowledge and understanding through thought, experience, and the senses". It encompasses all aspects of Intellect, intellectual functions and processes such as: perception, attentio ...
) - 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 encoding, encoded format for converting a specific type of data to displayable information. Content (media and publishing), Content formats are used in Sound recording and reproduction, recording and Telecommunication, transm ...
- a specific encoding format for converting a specific type of
data In the pursuit of knowledge, data (; ) is a collection of discrete values that convey information, describing quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interp ...
to
information Information is an Abstraction, abstract concept that refers to that which has the power to Communication, inform. At the most fundamental level information pertains to the Interpretation (logic), interpretation of that which may be sensed. ...
. *Text encoding uses a
markup language Markup language refers to a Encoding, text-encoding system consisting of a set of symbols inserted in a Text file, text document to control its structure, formatting, or the relationship between its parts. Markup is often used to control the dis ...
to tag the structure and other features of a text to facilitate processing by computers. (See also Text Encoding Initiative.) * 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 compression, lossy or Lossless com ...
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 Decoding methods, 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 ...
. * Neural encoding - the way in which information is represented in
neuron A neuron, neurone, or nerve cell is an membrane potential#Cell excitability, electrically excitable cell (biology), cell that communicates with other cells via specialized connections called synapses. The neuron is the main component of nervous ...
s. * Memory encoding - 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 supplementa ...
,
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 television, analog color television system that was used in France, some parts of Europe and Africa, and Russia ...
Other examples of decoding include: * Decoding (computer science) * Decoding methods, methods in communication theory for decoding codewords sent over a noisy channel *
Digital signal processing Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The digital signals processed in this manner are a ...
, the study of signals in a digital representation and the processing methods of these signals * Digital-to-analog converter, the use of analog circuit for decoding operations * Word decoding, the use of
phonics Phonics is a method for teaching people how to Reading, read and write an alphabetic language (such as English alphabet, English, Arabic alphabet, Arabic or Russian alphabet, Russian). It is done by demonstrating the relationship between the so ...
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 met ...
s and
writing system A writing system is a method of visually representing verbal communication, based on a script and a orthography, set of rules regulating its use. While both writing and spoken language, speech are useful in conveying messages, writing differs i ...
s are codes for human thought. International Air Transport Association airport codes are three-letter codes used to designate airports and used for bag tags. Station codes 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 A society is a group of individuals involved in persistent social ...
to mean "end of story", and has been used in other contexts to signify "the end".


See also

* Asemic writing *
Cipher In cryptography, a cipher (or cypher) is an algorithm for performing encryption or decryption—a series of well-defined steps that can be followed as a procedure. An alternative, less common term is ''encipherment''. To encipher or encode i ...
* Code (semiotics) * Equipment codes *
Quantum error correction Quantum error correction (QEC) is used in Quantum computer, quantum computing to protect quantum information from errors due to decoherence and other quantum noise. Quantum error correction is theorised as essential to achieve Quantum threshold the ...
*
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 Sign (semiotics), signs, where a sign is defined as anything that commun ...
* Universal language


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