Self-dual codes over commutative Frobenius rings
نویسندگان
چکیده
منابع مشابه
Self-dual codes over commutative Frobenius rings
We prove that self-dual codes exist over all finite commutative Frobenius rings, via their decomposition by the Chinese Remainder Theorem into local rings. We construct non-free self-dual codes under some conditions, using self-dual codes over finite fields, and we also construct free self-dual codes by lifting elements from the base finite field. We generalize the building-up construction for ...
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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 c = −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...
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Properties of matrix product codes over finite commutative Frobenius rings are investigated. The minimum distance of matrix product codes constructed with several types of matrices is bounded in different ways. The duals of matrix product codes are also explicitly described in terms of matrix product codes.
متن کاملMDS and self-dual codes over rings
In this paper we give the structure of constacyclic codes over formal power series and chain rings. We also present necessary and sufficient conditions on the existence of MDS codes over principal ideal rings. These results allow for the construction of infinite families of MDS self-dual codes over finite chain rings, formal power series and principal ideal rings.
متن کاملAnti-isomorphisms, character modules and self-dual codes over non-commutative rings
This paper is dedicated to Vera Pless. It is an elaboration on ideas of Nebe, Rains, and Sloane: by assuming the existence of an anti-isomorphism on a finite ring and by assuming a module alphabet has a well-behaved duality, one is able to study self-dual codes defined over alphabets that are modules over a non-commutative ring. Various examples are discussed.
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2010
ISSN: 1071-5797
DOI: 10.1016/j.ffa.2009.11.004