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Mathematical definition. In mathematical terms, the extended binary Golay code G24 consists of a 12-dimensional linear subspace W of the space V = F24. 2 of 24-bit words such that any two distinct elements of W differ in at least 8 coordinates. W is called a linear code because it is a vector space. In all, W comprises 4096 = 212 elements.
Parity-check matrix. In coding theory, a parity-check matrix of a linear block code C is a matrix which describes the linear relations that the components of a codeword must satisfy. It can be used to decide whether a particular vector is a codeword and is also used in decoding algorithms.
A linear code of length n and dimension k is a linear subspace C with dimension k of the vector space where is the finite field with q elements. Such a code is called a q -ary code. If q = 2 or q = 3, the code is described as a binary code, or a ternary code respectively. The vectors in C are called codewords.
The Evening Standard, formerly The Standard (1827–1904), is a local free daily newspaper in London, England, published Monday to Friday in tabloid format. In October 2009, after being purchased by Russian businessman Alexander Lebedev, the paper ended a 180-year history of paid circulation and became a free newspaper, doubling its circulation ...
C = 101. D = 100. Here the letter A has been assigned 2 bits, B has 1 bit, and C and D both have 3 bits. To make the code a canonical Huffman code, the codes are renumbered. The bit lengths stay the same with the code book being sorted first by codeword length and secondly by alphabetical value of the letter: B = 0. A = 11.
Locally decodable code. A locally decodable code ( LDC) is an error-correcting code that allows a single bit of the original message to be decoded with high probability by only examining (or querying) a small number of bits of a possibly corrupted codeword. [1] [2] [3] This property could be useful, say, in a context where information is being ...
Commercial code (communications) In telecommunication, a commercial code is a code once used to save on cablegram costs. [1] Telegraph (and telex) charged per word sent, so companies which sent large volumes of telegrams developed codes to save money on tolls. Elaborate commercial codes which encoded complete phrases into single words were ...
In coding theory, the Kraft–McMillan inequality gives a necessary and sufficient condition for the existence of a prefix code [1] (in Leon G. Kraft's version) or a uniquely decodable code (in Brockway McMillan 's version) for a given set of codeword lengths. Its applications to prefix codes and trees often find use in computer science and ...
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