Title: Constructions of self-dual codes over finite commutative chain rings

Authors: Steven T. Dougherty, Jon-Lark Kim, Hongwei Liu

Addresses: Department of Mathematics, University of Scranton, Scranton, PA 18510, USA. ' Department of Mathematics, University of Louisville, Louisville, KY 40292, USA. ' Department of Mathematics, Huazhong Normal University, Wuhan, Hubei 430079, China

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.

Keywords: chain rings; MDS codes; self-dual codes; Chinese remainder theorem; torsion codes.

DOI: 10.1504/IJICOT.2010.032133

International Journal of Information and Coding Theory, 2010 Vol.1 No.2, pp.171 - 190

Published online: 10 Mar 2010 *

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