On the Covering Radius of Ternary Extremal Self-Dual Codes

Authors:
Masaaki Harada;Michio Ozeki;Kenichiro Tanabe
Affiliations:
Department of Mathematical Sciences, Yamagata University, Yamagata 990-8560, Japan;Department of Mathematical Sciences, Yamagata University, Yamagata 990-8560, Japan;Institute of Mathematics, University of Tsukuba, Tsukuba 305-8571, Japan
Venue:
Designs, Codes and Cryptography
Year:
2004

Citing 4
Cited 0

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Extremal self-dual [40,20,8] codes with covering radius 7

Finite Fields and Their Applications

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Abstract

In this paper, we investigate the covering radius of ternary extremal self-dual codes. The covering radii of all ternary extremal self-dual codes of lengths up to 20 were previously known. The complete coset weight distributions of the two inequivalent extremal self-dual codes of length 24 are determined. As a consequence, it is shown that every extremal ternary self-dual code of length up to 24 has covering radius which meets the Delsarte bound. The first example of a ternary extremal self-dual code with covering radius which does not meet the Delsarte bound is also found. It is worth mentioning that the found code is of length 32.