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Title: On the algebraic structure of quasi-cyclic codes I : finite fields
Authors: Ling, San
Sole, Patrick
Keywords: DRNTU::Engineering::Computer science and engineering::Computing methodologies::Symbolic and algebraic manipulation
Issue Date: 2001
Source: Ling, S., & Solé, P. (2001). On the algebraic structure of quasi-cyclic codes I: Finite fields. IEEE Transactions on Information Theory, 47(7), 2751-2760.
Series/Report no.: IEEE transactions on information theory
Abstract: A new algebraic approach to quasi-cyclic codes is introduced. The key idea is to regard a quasi-cyclic code over a field as a linear code over an auxiliary ring. By the use of the Chinese remainder theorem (CRT), or of the discrete Fourier transform (DFT), that ring can be decomposed into a direct product of fields. That ring decomposition in turn yields a code construction from codes of lower lengths which turns out to be in some cases the celebrated squaring and cubing constructions and in other cases the (u+υ|u-υ) and Vandermonde constructions. All binary extended quadratic residue codes of length a multiple of three are shown to be attainable by the cubing construction. Quinting and septing constructions are introduced. Other results made possible by the ring decomposition are a characterization of self-dual quasi-cyclic codes, and a trace representation that generalizes that of cyclic codes.
ISSN: 0018-9448
DOI: 10.1109/18.959257
Rights: © 2001 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The published version is available at: [DOI:].
Fulltext Permission: open
Fulltext Availability: With Fulltext
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