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Code loops and even codes over F4

โœ Scribed by Masaaki Kitazume


Publisher
Elsevier Science
Year
1988
Tongue
English
Weight
414 KB
Volume
118
Category
Article
ISSN
0021-8693

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The natural analogues of Lee weight and the Gray map over % are introduced. Self-dual codes for the Euclidean scalar product with Lee weights multiple of 4 are called Type II. They produce Type II binary codes by the Gray map. All extended Q-codes of length a multiple of 4 are Type II. This includes

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The notion of a shadow of a self-dual binary code is generalized to self-dual codes over 9 . A Gleason formula for the symmetrized weight enumerator of the shadow of a Type I code is derived. Congruence properties of the weights follow; this yields constructions of self-dual codes of larger lengths

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A central problem in coding theory is that of finding the smallest length for which there exists a linear code of dimension k and minimum distance d, over a field of ~7 elements, We consider here the problem for quaternary codes (q=4), solving the problem for k< 3 for all values of d, and for k=4 fo