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Rank Error-correcting Code
In coding theory, rank codes (also called Gabidulin codes) are non-binaryCodes for which each input symbol is from a set of size greater than 2. linear error-correcting codes over not Hamming but ''rank'' metric. They described a systematic way of building codes that could detect and correct multiple random ''rank'' errors. By adding redundancy with coding ''k''-symbol word to a ''n''-symbol word, a rank code can correct any errors of rank up to ''t'' = ⌊ (''d'' − 1) / 2 ⌋, where ''d'' is a code distance. As an erasure code, it can correct up to ''d'' − 1 known erasures. A rank code is an algebraic linear code over the finite field GF(q^N) similar to Reed–Solomon code. The rank of the vector over GF(q^N) is the maximum number of linearly independent components over GF(q). The rank distance between two vectors over GF(q^N) is the rank of the difference of these vectors. The rank code corrects all errors with rank of the er ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Linear Block Code
In coding theory, block codes are a large and important family of error-correcting codes that encode data in blocks. There is a vast number of examples for block codes, many of which have a wide range of practical applications. The abstract definition of block codes is conceptually useful because it allows coding theorists, mathematicians, and computer scientists to study the limitations of ''all'' block codes in a unified way. Such limitations often take the form of ''bounds'' that relate different parameters of the block code to each other, such as its rate and its ability to detect and correct errors. Examples of block codes are Reed–Solomon codes, Hamming codes, Hadamard codes, Expander codes, Golay codes, Reed–Muller codes and Polar codes. These examples also belong to the class of linear codes, and hence they are called linear block codes. More particularly, these codes are known as algebraic block codes, or cyclic block codes, because they can be generated using ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Rank Error Correcting Code
In coding theory, rank codes (also called Gabidulin codes) are non-binaryCodes for which each input symbol is from a set of size greater than 2. linear error-correcting codes over not Hamming but ''rank'' metric. They described a systematic way of building codes that could detect and correct multiple random ''rank'' errors. By adding redundancy with coding ''k''-symbol word to a ''n''-symbol word, a rank code can correct any errors of rank up to ''t'' = ⌊ (''d'' − 1) / 2 ⌋, where ''d'' is a code distance. As an erasure code, it can correct up to ''d'' − 1 known erasures. A rank code is an algebraic linear code over the finite field GF(q^N) similar to Reed–Solomon code. The rank of the vector over GF(q^N) is the maximum number of linearly independent components over GF(q). The rank distance between two vectors over GF(q^N) is the rank of the difference of these vectors. The rank code corrects all errors with rank of the er ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Berlekamp–Massey Algorithm
The Berlekamp–Massey algorithm is an algorithm that will find the shortest linear-feedback shift register (LFSR) for a given binary output sequence. The algorithm will also find the minimal polynomial of a linearly recurrent sequence in an arbitrary field. The field requirement means that the Berlekamp–Massey algorithm requires all non-zero elements to have a multiplicative inverse. Reeds and Sloane offer an extension to handle a ring. Elwyn Berlekamp invented an algorithm for decoding Bose–Chaudhuri–Hocquenghem (BCH) codes. James Massey recognized its application to linear feedback shift registers and simplified the algorithm. Massey termed the algorithm the LFSR Synthesis Algorithm (Berlekamp Iterative Algorithm), but it is now known as the Berlekamp–Massey algorithm. Description of algorithm The Berlekamp–Massey algorithm is an alternative to the Reed–Solomon Peterson decoder for solving the set of linear equations. It can be summarized as finding the co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
