非线性等重检错好码的存在性的进一步分析

Further Analysis of the existence on Nonlinear Constant Weight and Good Error-detecting codes

二元 (n,2δ,w)非线性等重码在数字通信中被广泛地用作检错码 ,人们一直研究一般 (n,2δ,w)等重码成为检错好码的充要条件。首先讨论了二元 (n,2 δ,w)等重码成为检错好码的条件 ,得到了二元(n,2 δ,w)最优等重码成为检错好码的两个充分必要条件 ,以及 n≠ 2 w时 ,二元 (n,2 δ,w)最优等重码不是检错好码的结论 ,同时 ,还讨论了 q元非线性等重检错好码的存在性 。

Binary nonlinear codes(n,2δ,w)are widely used as error detecting codes in digital communication and as good error-detecting codes, the sufficient and necessary condition of (n,2δ,w) codes has been studied by many people. In this paper, the condition of (n,2δ,w) codes as good error-detecting codes is discussed, then two sufficient and necessary conditions of (n,2δ,w) optimal constant weight codes and the conclusion that n≠2w (n,2δ,w)optimal constant weight codes is not good error-detecting codes are obtained. At the same time, the existence of q-ary nonlinear constant weight codes and good error-detecting codes is discussed, and some new results are also obtained.