Construction of self-dual codes over finite rings Zpm

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:115

Article

Lee, Heisook¹  Lee, Yoonjin¹ 

[1] Ewha Womans Univ, Dept Math, Seoul 120750, South Korea

关键词: self-dual codes;    self-orthogonal codes;    finite ring;    MDS codes;    near MDS;    MDR codes;    near MDR codes;   

DOI  :  10.1016/j.jcta.2007.07.001

来源: Elsevier

【 摘 要 】

We present an efficient method for constructing self-dual or self-orthogonal codes over finite rings Z(pm) (or Z(m)) with p an odd prime and m a positive integer. This is an extension of the previous work [J.-L. Kim, Y. Lee, Euclidean and Hermitian self-dual MDS codes over large finite fields, J. Combin. Theory Ser. A 105 (2004) 79-95] over large finite fields GF(p(m)) to finite rings Z(pm) (or Z(m)). Using this method we construct self-dual or self-orthogonal codes of length at least up to 10 over various finite rings Z(pm) or Z(pq) with q an odd prime, where p(m) = 25, 125, 169, 289 and pq = 65, 85. All the self-dual codes we obtained are MDS, MDR, near MDS, or near MDR codes. (C) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free