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Please use this identifier to cite or link to this item: http://eprint.iitd.ac.in/handle/2074/1733

Title: Algebraic characterization of MDS group codes over cyclic groups
Authors: Zain, A A
Rajan, B S
Keywords: group codes
MDS codes
dual codes
cyclic groups
Issue Date: 1995
Citation: Information Theory, IEEE Transactions on, 41(6), 2052 - 2056p.
Abstract: An (n,k) group code over a group G is a subset of Gn which forms a group under componentwise group operation and can be defined in terms of n-k homomorphisms from Gk to G. 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 endomorphisms of G. A matrix is associated with the k(n-k) defining endomorphisms of the code and necessary and sufficient conditions for this matrix to define an MDS code over cyclic groups is proved. Using this matrix characterization it is proved that over a cyclic group with M elements, where M=p1d(1)p2d(2) ···pmd(m),(k+s,k) MDS group codes, for all s,k⩾2, do not exist if max {s,k}⩾min {p1,p2,··,pm}. Finally, it is shown that the dual code of an MDS group code over CM, a cyclic group with M elements, is also an MDS group code
URI: http://eprint.iitd.ac.in/dspace/handle/2074/1733
Appears in Collections:Electrical Engineering

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