Self-dual Codes over the Kleinian Four Group

Details Self-dual Codes over the Kleinian Four Group Self-dual Codes over the Kleinian Four Group

2000-05-26

arxiv.org/abs/math/0005266v1

Mathematische Annalen 327 (2003), 227-255

Mathematics

Combinatorics

26 pages with 5 tables and 1 figure, LaTeX

Scientific paper

We introduce self-dual codes over the Kleinian four group K = Z_2 x Z_2 for a natural quadratic form on K^n and develop the theory. Topics studied are: weight enumerators, mass formulas, classification up to length 8, neighbourhood graphs, extremal codes, shadows, generalized t-designs, lexicographic codes, the Hexacode and its odd and shorter cousin, automorphism groups, marked codes. Kleinian codes form a new and natural fourth step in a series of analogies between binary codes, lattices and vertex operator algebras. This analogy will be emphasized and explained in detail.

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