Abstract / truncated to 115 words (read the full abstract)

A counting sequence of length n is a list of all 2^n binary n-tuples (binary codewords of length n). The number of bit positions where two codewords differ is called the Hamming distance of these two codewords. The average Hamming distance of a counting sequence of length n is defined as the average Hamming distance between the 2^n pairs of successive codewords, including the pair of the last and the first codeword. A counting sequence of length n which has average Hamming distance equal to n-1/2 is called a maximum counting sequence. The number of bit changes in bit position i, in a counting sequence of length n is called the transition count of bit ... toggle 11 keywords

complete graph – counting sequence – gray code – greedy algorithm – lexicode – linearity – maximum counting sequence – self-orthogonality – self-duality – separability – uniform counting sequence

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