## 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 |
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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 |