DocumentCode
1474570
Title
Type II codes over F2+uF2
Author
Dougherty, Steven T. ; Gaborit, Philippe ; Harada, Masaaki ; Solé, Patrick
Author_Institution
Dept. of Math., Univ. of Scranton, PA, USA
Volume
45
Issue
1
fYear
1999
fDate
1/1/1999 12:00:00 AM
Firstpage
32
Lastpage
45
Abstract
The alphabet F2+uF2 is viewed here as a quotient of the Gaussian integers by the ideal (2). Self-dual F2 +uF2 codes with Lee weights a multiple of 4 are called Type II. They give even unimodular Gaussian lattices by Construction A, while Type I codes yield unimodular Gaussian lattices. Construction B makes it possible to realize the Leech lattice as a Gaussian lattice. There is a Gray map which maps Type II codes into Type II binary codes with a fixed point free involution in their automorphism group. Combinatorial constructions use weighing matrices and strongly regular graphs. Gleason-type theorems for the symmetrized weight enumerators of Type II codes are derived. All self-dual codes are classified for length up to 8. The shadow of the Type I codes yields bounds on the highest minimum Hamming and Lee weights
Keywords
Gaussian processes; binary codes; dual codes; graph theory; lattice theory; matrix algebra; Construction A; Construction B; Gaussian integers; Gleason-type theorems; Gray map; Lee weights; Leech lattice; Type II codes; automorphism group; binary codes; combinatorial constructions; even unimodular Gaussian lattices; fixed point free involution; minimum Hamming weight; regular graphs; self-dual F2+uF2 codes; self-dual codes; shadow; symmetrized weight enumerators; weighing matrices; Binary codes; Lattices; Mathematics;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/18.746770
Filename
746770
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