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An elementary construction of codes from the groups of units of residue rings of polynomials

In this note, we present an elementary verification of the minimum distance of some codes constructed by Xing (2002). We show that the codes obtained from this construction are subsets of cosets of linear codes with a given parity-check matrix.

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Published in:	IEEE transactions on information theory 2005-01, Vol.51 (1), p.419-420
Main Authors:	Reid, L., Wickham, C.
Format:	Article
Language:	English
Subjects:	Applied sciences Character generation Codes Coding, codes Construction Exact sciences and technology Galois fields Induction generators Information systems Information theory Information, signal and communications theory Linear code Mathematics Parity check codes Polynomials residue rings Residues Signal and communications theory Telecommunications and information theory units
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creator	Reid, L. Wickham, C.
description	In this note, we present an elementary verification of the minimum distance of some codes constructed by Xing (2002). We show that the codes obtained from this construction are subsets of cosets of linear codes with a given parity-check matrix.
doi_str_mv	10.1109/TIT.2004.839540
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source	IEEE Electronic Library (IEL) Journals
subjects	Applied sciences Character generation Codes Coding, codes Construction Exact sciences and technology Galois fields Induction generators Information systems Information theory Information, signal and communications theory Linear code Mathematics Parity check codes Polynomials residue rings Residues Signal and communications theory Telecommunications and information theory units
title	An elementary construction of codes from the groups of units of residue rings of polynomials
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