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$F_q$-Linear Cyclic Codes over $F_{qm}$:DFT Characterization

Dey, Bikash Kumar and Rajan, Sundar B (2001) $F_q$-Linear Cyclic Codes over $F_{qm}$:DFT Characterization. In: 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC-14), November 26–30, Melbourne, Australia, pp. 67-76.

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Codes over $F_{qm}$ that form vector spaces over $F_q$ are called $F_q$-linear codes over $F_{qm}$. Among these we consider only cyclic codes and call them $F_q$-linear cyclic codes ($F_q$LC codes) over $F_{qm}$. This class of codes includes as special cases (i) group cyclic codes over elementary abelian groups (q = p, a prime), (ii) subspace subcodes of Reed-Solomon codes and (iii) linear cyclic codes over $F_q$ (m=1). Transform domain characterization of $F_q$LC codes is obtained using Discrete Fourier Transform (DFT) over an extension field of $F_{qm}$. We showho wone can use this transform domain structures to estimate a minimum distance bound for the corresponding quasicyclic code by BCH-like argument.

Item Type: Conference Paper
Publication: Lecture Notes in Computer Science-Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Publisher: Springer
Additional Information: Copyright of this article belongs to Springer.
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited: 18 Jul 2008
Last Modified: 19 Sep 2010 04:47
URI: http://eprints.iisc.ac.in/id/eprint/15110

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