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Type II codes over F2+uF2

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4 Author(s)
Dougherty, S.T. ; Dept. of Math., Univ. of Scranton, PA, USA ; Gaborit, P. ; Harada, M. ; Sole, P.

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

Published in:

Information Theory, IEEE Transactions on  (Volume:45 ,  Issue: 1 )

Date of Publication:

Jan 1999

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