Double and bordered alpha-circulant self-dual codes over finite commutative chain rings

In this paper we investigate codes over finite commutative rings R, whose generator matrices are built from alpha-circulant matrices. For a non-trivial ideal I < R we give a method to lift such codes over R/I to codes over R, such that some isomorphic copies are avoided. For the case where I is the minimal ideal of a finite chain ring we refine this lifting method: We impose the additional restriction that lifting preserves self-duality. It will be shown that this can be achieved by solving a liIn this paper we investigate codes over finite commutative rings R, whose generator matrices are built from alpha-circulant matrices. For a non-trivial ideal I < R we give a method to lift such codes over R/I to codes over R, such that some isomorphic copies are avoided. For the case where I is the minimal ideal of a finite chain ring we refine this lifting method: We impose the additional restriction that lifting preserves self-duality. It will be shown that this can be achieved by solving a linear system of equations over a finite field. Finally we apply this technique to Z_4-linear double nega-circulant and bordered circulant self-dual codes. We determine the best minimum Lee distance of these codes up to length 64.show moreshow less

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Metadaten
Institutes:Mathematik
Author: Michael Kiermaier, Alfred Wassermann
Year of Completion:2008
SWD-Keyword:Codierungstheorie
Tag:Lee metric; circulant matrix; finite chain ring; linear code over rings; self-dual code
Dewey Decimal Classification:510 Mathematik
MSC-Classification:11T71 Algebraic coding theory; cryptography
URN:urn:nbn:de:bvb:703-opus-4501
Source:Proceedings of the Eleventh International Workshop on Algebraic and Combinatorial Coding Theory (ACCT-2008)
Document Type:Article
Language:English
Date of Publication (online):02.07.2008