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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.
Code word (communication) 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, clarity, brevity, or secrecy.
A book cipher is a cipher in which each word or letter in the plaintext of a message is replaced by some code that locates it in another text, the key . A simple version of such a cipher would use a specific book as the key, and would replace each word of the plaintext by a number that gives the position where that word occurs in that book.
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In mathematical terms, Hamming codes are a class of binary linear code. For each integer r ≥ 2 there is a code-word with block length n = 2r − 1 and message length k = 2r − r − 1. Hence the rate of Hamming codes is R = k / n = 1 − r / (2r − 1), which is the highest possible for codes with minimum distance of three (i.e., the minimal ...
A code over an alphabet Q of size |Q| = q is called q-ary R-covering code of length n if for every word there is a codeword such that the Hamming distance (,). In other words, the spheres (or balls or rook-domains) of radius R with respect to the Hamming metric around the codewords of C have to exhaust the finite metric space Q n {\displaystyle ...
Add a letter and crack the code! Add a letter and crack the code!