Quasi-Cyclic Dyadic Codes in the Walsh-Hadamard Transform Domain

Rajan, Sundar B and Lee, Moon Ho (2002) Quasi-Cyclic Dyadic Codes in the Walsh-Hadamard Transform Domain. In: IEEE Transactions on Information Theory, 48 (8). 2406 -2412.

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Abstract

A code is s-quasi-cyclic (s-QC) if there is an integer s such that cyclic shift of a codeword by s-positions is also a codeword. For s = 1, cyclic codes are obtained. A dyadic code is a code which is closed under all dyadic shifts. An s-QC dyadic (s-QCD) code is one which is both s-QC and dyadic. QCD codes with s = 1 give codes that are cyclic and dyadic (CD). We obtain a simple characterization of all QCD codes (hence of CD codes) over any field of odd characteristic using Walsh-Hadamard transform defined over that finite field. Also, it is shown that dual a code of an s-QCD code is also an s-QCD code and s-QCD codes for a given dimension are enumerated for all possible values of s.

Item Type:	Journal Article
Publication:	IEEE Transactions on Information Theory
Publisher:	IEEE
Additional Information:	Copyright 1990 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Keywords:	Discrete Fourier transform (DFT);Dyadic codes;Quasicyclic (QC) codes;Walsh–Hadamard transform (WHT)
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	16 Jan 2006
Last Modified:	19 Sep 2010 04:22
URI:	http://eprints.iisc.ac.in/id/eprint/5022

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