Constructions of self-dual codes over finite commutative chain rings. (11th March 2010)

• Record Type: Journal Article
• Authors: Dougherty, Steven T.; Kim, Jon-Lark; Liu, Hongwei
• Is Part Of: International journal of information and coding theory. Volume 1:Number 2(2010)
• Page Start: 171
• Page End: 190
• Publication Date: 2010-03-11
• Subjects: chain rings -- MDS codes -- self-dual codes -- Chinese remainder theorem -- torsion codes; Coding theory -- Periodicals; Information theory -- Periodicals; 003.54
• Languages: English
• ISSNs: 1753-7703

Abstract

We study self-dual codes over chain rings. We describe a technique for constructing new self-dual codes from existing codes and we prove that for chain rings containing an element c with c² = −1, all self-dual codes can be constructed by this technique. We extend this construction to self-dual codes over principal ideal rings via the Chinese Remainder Theorem. We use torsion codes to describe the structure of self-dual codes over chain rings and to set bounds on their minimum Hamming weight. Interestingly, we find the first examples of MDS self-dual codes of lengths 6 and 8 and near-MDS self-dual codes of length 10 over a certain chain ring which is not a Galois ring.