Construction of cubic self-dual codes

Authors:
Sunghyu Han;Jon-Lark kim;Heisook Lee;Yoonjin Lee
Affiliations:
School of Liberal Arts, Korea University of Technology and Education, Cheonan, South Korea;Department of Mathematics, University of Louisville, Louisville, KY;Department of Mathematics, Ewha Womans University, Seoul, South Korea;Department of Mathematics, Ewha Womans University, Seoul, South Korea
Venue:
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
Year:
2009

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Abstract

We present a building-up construction method for quasi-cyclic self-dual codes over finite fields. By using this, we give cubic (i.e., l-quasi-cyclic codes of length 3l) self-dual codes over various finite fields, which are optimal or have the best known parameters. In particular, we find a new quasi-cyclic self-dual [24, 12, 9] code over F5, whose corresponding lattice by Construction A is shown to be the odd Leech lattice O24. Only one self-dual [24, 12, 9] code over F5 was known before up to monomial equivalence.