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

Authors:	Steven T Dougherty T Aaron Gulliver Masaaki Harada

Institution:	(1) Department of Mathematics, University of Scranton, Scranton, PA, 18510;(2) Department of Electrical and Electronic Engineering, University of Canterbury, Private Bag, 4800 Christchurch, New Zealand;(3) Department of Mathematical Sciences, Yamagata University, Yamagata, 990, Japan

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

Keywords:	self-dual code over finite ring Type II code double circulant code even unimodular lattice
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