Transform Domain Characterization of Dual Group Codes of Cyclic Group Codes over Elementary Abelian Groups
نویسندگان
چکیده
منابع مشابه
Quasideterminant Characterization of MDS Group Codes over Abelian Groups
A group code defined over a group G is a subset of Gn which forms a group under componentwise group operation. The well known matrix characterization of MDS (Maximum Distance Separable) linear codes over finite fields is generalized to MDS group codes over abelian groups, using the notion of quasideterminants defined for matrices over non-commutative rings.
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An (n, k) group code over a group G is a subset of G which forms a group under componentwise group operation and can be defined in terms of n — k homomorphisms from G to G. In this correspondence, the set of homomorphisms which define Maximum Distance Separable (MDS) group codes defined over cyclic groups are characterized. Each defining homomorphism can be specified by a set of k endomorpbisms...
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Abelian codes constitute a class of codes that includes cyclic codes as a special case. It is shown that the general class of abelian codes can be characterized in the transform domain using discrete Fourier transform (DFT) over finite fields with appropriate mixed radix Manuscript received July 31, 1991. B. S. Rajan is with the Electrical Engineering Department, Indian Institute of Technology,...
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We prove a general form of bit flip formula for the quantum Fourier transform on finite abelian groups and use it to encode some general CSS codes on these groups.
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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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ژورنال
عنوان ژورنال: Sultan Qaboos University Journal for Science [SQUJS]
سال: 2009
ISSN: 2414-536X,1027-524X
DOI: 10.24200/squjs.vol14iss0pp53-59