NDLI: Type II codes over Z/sub 4/

Content Provider	IEEE Xplore Digital Library
Author	Bonnecaze, A. Sole, P. Bachoc, C. Mourrain, B.
Copyright Year	1997
Description	Author affiliation: CNRS, Sophia Antipolis, France (Bonnecaze, A.)
Abstract	The conditions satisfied by the weight enumerator of self-dual codes, defined over the ring of integers module four, have been studied by Klemm (1989), then by Conway and Sloane (1993). The MacWilliams (1977) transform determines a group of substitutions, each of which fixes the weight enumerator of a self-dual code. This weight enumerator belongs to the ring of polynomials fixed by the group of substitutions, called the ring R of invariants. Among all of the quaternary self-dual codes, some have the property that all euclidean weights are multiples of 8. These codes are called type II codes by analogy with the binary case. An upper bound on their minimum euclidean weight is given, thereby leading to a natural notion of extremality akin to similar concepts for type II binary codes and type II lattices. The most interesting examples of type II codes are perhaps the extended quaternary quadratic residue codes. This class of codes includes the octacode [8, 4, 6] and the lifted Golay [24, 12, 12]. Other classes of interest comprise a multilevel construction from binary Reed-Muller and lifted double circulant codes.
File Size	97951
File Format	PDF
ISBN	0780339568
DOI	10.1109/ISIT.1997.613114
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1997-06-29
Publisher Place	Germany
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Lattices Combinatorial mathematics Euclidean distance Error correction codes Algebra
Content Type	Text
Resource Type	Article

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