Note on the g-fold Joint Weight Enumerators of Self-Dual Codes over ℤ k |
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| Authors: | Steven T. Dougherty Masaaki Harada Manabu Oura |
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| Affiliation: | (1) Department of Mathematics, University of Scranton, Scranton, PA 18510, USA (e-mail: harada@kszaoh3.kj.yamagata-u.ac.jp), US;(2) Department of Mathematical Sciences, Yamagata University, Yamagata 990-8560, Japan (e-mail: doughertys1@tiger.uofs.edu), JP;(3) Graduate School of Mathematics, Kyushu University, Fukuoka 812-8581, Japan (e-mail: ohura@math.kyushu-u.ac.jp), JP |
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| Abstract: | Recently there has been interest in self-dual codes over finite rings. In this note, g-fold joint weight enumerators of codes over the ring ℤ k of integers modulo k are introduced as a generalization of the biweight enumerators. We establish the MacWilliams relations for these weight enumerators and investigate the biweight enumerators of self-dual codes over ℤ k . We derive Gleason-type theorems for the corresponding biweight enumerators with the help of invariant theory. Received: March 13, 2000; revised version: December 11, 2000 |
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| Keywords: | : Self-dual codes g-fold joint weight enumerators MacWilliams relations. |
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