Divisibility properties for covering radius of certain cyclic codes

We are presenting a new method to obtain the covering radius of codes and in particular to prove quasi-perfection in codes. Our techniques combine divisibility results of Ax-Katz and Moreno-Moreno as well as coding theoretic methods. We answer a problem posed by Cohen-Honkala-Litsyn-Lobstein in the...

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Bibliographic Details
Published in:IEEE transactions on information theory 2003-12, Vol.49 (12), p.3299-3303
Main Authors: Moreno, O., Castro, F.N.
Format: Article
Language:English
Subjects:
Codes
Coding
Computer science
Covering
Equations
Finite element analysis
Galois fields
Information theory
Mathematics
Polynomials
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Summary:We are presenting a new method to obtain the covering radius of codes and in particular to prove quasi-perfection in codes. Our techniques combine divisibility results of Ax-Katz and Moreno-Moreno as well as coding theoretic methods. We answer a problem posed by Cohen-Honkala-Litsyn-Lobstein in the book covering radius for Bose-Chaudhuri-Hocquenghem (BCH) codes. We also obtain the covering radius for many new classes of codes.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2003.820033