2014/06/23 by Masao Kasahara, Kasahara, Masao, Shigeichi Hirasawa +1
Computer Science · Mathematics · #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1406.5797
arxiv created 2014/06/23 · arxiv updated 2014/06/24
A new method of constructing optimum constant weight codes over F2 based on a generalized (u, u+v) construction is presented. We present a new method of constructing superimposed code C(s1,s2,⋯,sI)(h1, h2, ⋯, hI) bound. and presented a large class of optimum constant weight codes over F2 that meet the bound due to Brouwer and Verhoeff, which will be referred to as BV . We present large classes of optimum constant weight codes over F2 for k=2 and k=3 for n \leqq 128. We also present optimum constant weight codes over F2 that meet the BV bound for k=2,3,4,5 and 6, for n \leqq 128. The authors would like to present the following conjectures : CI: C(s1)(h1) presented in this paper yields the optimum constant weight codes for the code-length n=3h1, number of information symbols k=2 and minimum distance d=2h1 for any positive integer h1. CII: C(s1)(h1) yields the optimum constant weight codes at n=7h1, k=3 and d=4h1 for any h1. CIII: Code C(s1,s2,⋯,sI)(h1, h2, ⋯, hI) yields the optimum constant weight codes of length n=2k+1-2, and minimum distance d=2k for any number of information symbols k≥ 3.