Asymptotic bound on binary self-orthogonal codes  

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

出　　处：《Science China Mathematics》2009年第4期631-638,共8页中国科学：数学（英文版）

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)

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.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 information 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.

关 键 词：algebraic geometry codes concatenated codes Gilbert-Varshamov bound Reed-Muller codes self-dual basis self-orthogonal codes 11T71 

分 类 号：O157.4[理学—数学]