Group matrix ring codes and constructions of self-dual codes
نویسندگان
چکیده
منابع مشابه
Arithmetic Constructions Of Binary Self-Dual Codes
The goal of this thesis is to explore the interplay between binary self-dual codes and the \'etale cohomology of arithmetic schemes. Three constructions of binary self-dual codes with arithmetic origins are proposed and compared: Construction $\Q$, Construction G and the Equivariant Construction. In this thesis, we prove that up to equivalence, all binary self-dual codes of length at least $4$ ...
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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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Recently, codes over some special finite rings especially chain rings have been studied. More recently, codes over finite non-chain rings have been also considered. Study on codes over such rings or rings in general is motivated by the existence of some special maps called Gray maps whose images give codes over fields. Quantum error-correcting (QEC) codes play a crucial role in protecting quantum ...
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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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ژورنال
عنوان ژورنال: Applicable Algebra in Engineering, Communication and Computing
سال: 2021
ISSN: 0938-1279,1432-0622
DOI: 10.1007/s00200-021-00504-9