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  2. Hamming code - Wikipedia

    en.wikipedia.org/wiki/Hamming_code

    Hence the rate of Hamming codes is R = k / n = 1 − r / (2 r − 1), which is the highest possible for codes with minimum distance of three (i.e., the minimal number of bit changes needed to go from any code word to any other code word is three) and block length 2 r − 1.

  3. Lexicographic code - Wikipedia

    en.wikipedia.org/wiki/Lexicographic_code

    The theory of lexicographic codes is closely connected to combinatorial game theory. In particular, the codewords in a binary lexicographic code of distance d encode the winning positions in a variant of Grundy's game , played on a collection of heaps of stones, in which each move consists of replacing any one heap by at most d − 1 smaller ...

  4. Hamming (7,4) - Wikipedia

    en.wikipedia.org/wiki/Hamming(7,4)

    It is a member of a larger family of Hamming codes, but the term Hamming code often refers to this specific code that Richard W. Hamming introduced in 1950. At the time, Hamming worked at Bell Telephone Laboratories and was frustrated with the error-prone punched card reader, which is why he started working on error-correcting codes.

  5. Hamming space - Wikipedia

    en.wikipedia.org/wiki/Hamming_space

    In coding theory, if Q has q elements, then any subset C (usually assumed of cardinality at least two) of the N-dimensional Hamming space over Q is called a q-ary code of length N; the elements of C are called codewords. [4] [5] In the case where C is a linear subspace of its Hamming space, it is called a linear code. [4]

  6. List of algebraic coding theory topics - Wikipedia

    en.wikipedia.org/wiki/List_of_algebraic_coding...

    Algebraic geometry code; BCH code; BCJR algorithm; Belief propagation; Berger code; Berlekamp–Massey algorithm; Binary Golay code; Binary Goppa code; Bipolar violation; CRHF; Casting out nines; Check digit; Chien's search; Chipkill; Cksum; Coding gain; Coding theory; Constant-weight code; Convolutional code; Cross R-S code; Cryptographic hash ...

  7. Hamming distance - Wikipedia

    en.wikipedia.org/wiki/Hamming_distance

    For a fixed length n, the Hamming distance is a metric on the set of the words of length n (also known as a Hamming space), as it fulfills the conditions of non-negativity, symmetry, the Hamming distance of two words is 0 if and only if the two words are identical, and it satisfies the triangle inequality as well: [2] Indeed, if we fix three words a, b and c, then whenever there is a ...

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  9. Hamming graph - Wikipedia

    en.wikipedia.org/wiki/Hamming_graph

    The Hamming graph H(d,q) has vertex set S d, the set of ordered d-tuples of elements of S, or sequences of length d from S. Two vertices are adjacent if they differ in precisely one coordinate; that is, if their Hamming distance is one. The Hamming graph H(d,q) is, equivalently, the Cartesian product of d complete graphs K q. [1]

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