Type II Self-Dual Codes over Finite Rings and Even Unimodular Lattices

Authors:
Steven T. Dougherty;T. Aaron Gulliver;Masaaki Harada
Affiliations:
Department of Mathematics, University of Scranton, Scranton, PA 18510. doughertys@tiger.uofs.edu;Department of Electrical and Electronic Engineering, University of Canterbury, Private Bag 4800, Christchurch, New Zealand. gulliver@elec.canterbury.ac.nz;Department of Mathematical Sciences, Yamagata University, Yamagata 990, Japan. mharada@sci.kj.yamagatau.ac.jp
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
1999

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Abstract

In this paper, we investigate self-dual codes over finite rings,specifically the ring {\bb Z}2m of integers modulo 2m. Type II codes over{\bb Z}2m are introduced as self-dual codes with Euclidean weights which are a multiple of 2m +1. We describe a relationshipbetween Type II codes and even unimodular lattices. This relationship provides much information on Type II codes. Double circulant Type II codes over {\bb Z}2mare also studied.