On Upper Bounds for Minimum Distance and Covering Radiusof Non-binary Codes

Authors:
Tero Laihonen;Simon Litsyn
Affiliations:
Department of Mathematics, University of Turku, FIN-20500 Turku, Finland. E-mail: terolai@sara.cc.utu.fi;Department of EE-systems, Tel-Aviv University, Ramat-Aviv 69978 Israel. E-mail: litsyn@eng.tau.ac.il
Venue:
Designs, Codes and Cryptography
Year:
1998

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Abstract

We consider upper bounds on two fundamental parametersof a code; minimum distance and covering radius. New upper boundson the covering radius of non-binary linear codes are derivedby generalizing a method due to S. Litsyn and A. Tietäväinenlt:newu and combining it with a new upper bound on the asymptoticinformation rate of non-binary codes. The upper bound on theinformation rate is an application of a shortening method ofa code and is an analogue of the Shannon-Gallager-Berlekamp straightline bound on error probability. These results improve on thebest presently known asymptotic upper bounds on minimum distanceand covering radius of non-binary codes in certain intervals.