Self-dual codes over the Kleinian four group

By Gerald Höhn. 2000

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Abstract.We introduce self-dual codes over the Kleinian four group K=Z2×Z2 for a natural quadratic form on Kn 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.

Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/f7b31427e52d07234bcb66c874ab9003491b2629