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.…
| 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 |
