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_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_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 isin N, here N denotes natural number set. We show that 1) E_q (n,d,w) les qn, 2) Q_q (n,d) les qn+1, when q > 2, and if q=2, then 3) E_q (n,d,w) les n, 4) Q_q (n,d) les n+1