Constructions of A Large Class of Optimum Constant Weight Codes over F_2

Abstract

A new method of constructing optimum constant weight codes over F2 based on a generalized (u,u + v) construction [1]∼ [3] is presented. We present a new method of constructing superimposed code C (h1,h2,··· ,hI) (s1,s2,··· ,sI) bound. and presented a large class of optimum constant weight codes over F2 that meet the bound due to Brouwer and Verhoeff [4], 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 ≦ 128. We also present optimum constant weight codes over F2 that meet the BV bound [4] for k = 2, 3, 4, 5 and 6, for n ≦ 128. The authors would like to present the following conjectures : CI : C (h1) (s1) 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 (h1) (s1) yields the optimum constant weight codes at n = 7h1, k = 3 and d = 4h1 for any h1. CIII : Code C (h1,h2,··· ,hI) (s1,s2,··· ,sI) yields the optimum constant weight codes of length n = 2 − 2, and minimum distance d = 2 for any number of information symbols k ≥ 3. keyword Optimum code, Constant weight code, Brouwer·Verhoef bound, (u,u+ v) construction

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Cite this paper

@article{Kasahara2014ConstructionsOA, title={Constructions of A Large Class of Optimum Constant Weight Codes over F_2}, author={Masao Kasahara and Shigeichi Hirasawa}, journal={CoRR}, year={2014}, volume={abs/1406.5797} }