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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Bibliographic Details
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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Description
Summary: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.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2004.839540