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
fDate :
1/1/1999 12:00:00 AM
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;
Journal_Title :
Information Theory, IEEE Transactions on
