Double bordered constructions of self-dual codes from group rings over 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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MICHAEL KIERMAIER, ALFRED WASSERMANN michael.kiermaier, [email protected] Mathematical Department, University of Bayreuth, D-95440 Bayreuth, GERMANY Abstract. In this paper we investigate codes over finite commutative rings R, whose generator matrices are built from α-circulant matrices. For a non-trivial ideal I < R we give a method to lift such codes over R/I to codes over R, ...
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We give constructions of self-dual and formally self-dual codes from group rings where the ring is a finite commutative Frobenius ring. We improve the existing construction given in [11] by showing that one of the conditions given in the theorem is unnecessary and moreover it restricts the number of self-dual codes obtained by the construction. We show that several of the standard constructions...
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In this work, we propose a modified four circulant construction for self-dual codes and a bordered version of the construction using the properties of λ-circulant and λ-reverse circulant matrices. By using the constructions on F2, we obtain new binary codes of lengths 64 and 68. We also apply the constructions to the ring R2 and considering the F2 and R1-extensions, we obtain new singly-even ex...
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ژورنال
عنوان ژورنال: Cryptography and Communications
سال: 2020
ISSN: 1936-2447,1936-2455
DOI: 10.1007/s12095-019-00420-3