Optimal conflict-avoiding codes of length n ≡ 0 (mod 16) and weight 3
Designs, Codes and Cryptography
A tight asymptotic bound on the size of constant-weight conflict-avoiding codes
Designs, Codes and Cryptography
A general upper bound on the size of constant-weight conflict-avoiding codes
IEEE Transactions on Information Theory
Optimal conflict-avoiding codes of even length and weight 3
IEEE Transactions on Information Theory
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The paper deals with the problem of constructing a code of the maximum possible cardinality consisting of binary vectors of length n and Hamming weight 3 and having the following property: any 3 脳 n matrix whose rows are cyclic shifts of three different code vectors contains a 3 脳 3 permutation matrix as a submatrix. This property (in the special case w = 3) characterizes conflict-avoiding codes of length n for w active users, introduced in [1]. Using such codes in channels with asynchronous multiple access allows each of w active users to transmit a data packet successfully in one of w attempts during n time slots without collisions with other active users. An upper bound on the maximum cardinality of a conflict-avoiding code of length n with w = 3 is proved, and constructions of optimal codes achieving this bound are given. In particular, there are found conflict-avoiding codes for w = 3 which have much more vectors than codes of the same length obtained from cyclic Steiner triple systems by choosing a representative in each cyclic class.