Asymptotic bound on binary self-orthogonal codes

作     者：DING Yang Department of Mathematics, Southeast University, Nanjing 210096, China 

作者机构：Department of Mathematics Southeast University Nanjing China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2009年第52卷第4期

页      面：631-638页

核心收录：

学科分类：11[军事学] 1105[军事学-军队指挥学] 110505[军事学-密码学] 0701[理学-数学] 

基　　金：supported by the China Scholarship Council, National Natural Science Foundation of China(Grant No.10571026) the Cultivation Fund of the Key Scientific and Technical Innovation Project of Ministry of Education of China the Specialized Research Fund for the Doctoral Program of Higher Education (GrantNo. 20060286006) 

主　　题：algebraic geometry codes concatenated codes Gilbert-Varshamov bound Reed-Muller codes self-dual basis self-orthogonal codes 11T71 

摘      要：We present two constructions for binary self-orthogonal codes. It turns out that our constructions yield a constructive bound on binary self-orthogonal codes. In particular, when the in-formation rate R = 1/2, by our constructive lower bound, the relative minimum distance δ≈ 0.0595 (for GV bound, δ≈ 0.110). Moreover, we have proved that the binary self-orthogonal codes asymptotically achieve the Gilbert-Varshamov bound.