Construction of constant weight code and some upper bounds

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 Q/sub q/ (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 E/sub q/ (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 /spl isin/ N, here N denotes natural number set. We show that 1) E/sub q/ (n,d,w) /spl les/ qn, 2) Q/sub q/ (n,d) /spl les/ qn+1, when q > 2, and if q=2, then 3) E/sub q/ (n,d,w) /spl les/ n, 4) Q/sub q/ (n,d) /spl les/ n+1.