Abstract :
Properties of m-sequence are derived, based on the properties, a family of binary nonlinear constant weight codes is presented, these binary nonlinear constant weight codes can be employed in automatic repeat request (ARQ) communication system. In addition, let Qq (n,d) denote the maximal possible number of codewords in any q-ary equidistant code of length n and Hamming distance d between codewords (with no restriction on weight), let Eq (n,d,w) denote the largest possible number of codewords in any q-ary equidistant code with constant weight, length n, constant weight w, Hamming distance d between codewords. Let q, n, d, w isin N, here N denotes natural number set. We show that 1) Eq (n,d,w) les qn, 2) Qq (n,d) les qn+1, when q > 2, and if q=2, then 3) Eq (n,d,w) les n, 4) Qq (n,d) les n+1
Keywords :
Hamming codes; automatic repeat request; binary codes; m-sequences; nonlinear codes; set theory; Hamming distance; automatic repeat request communication system; binary nonlinear constant weight codes; constant weight code construction; m-sequence properties; natural number set; q-ary equidistant code; upper bounds; Automatic repeat request; Codes; Hamming distance; Hamming weight; Signal detection; Upper bound;
