A new class of codes over Z_2 x Z_2

Details A new class of codes over Z_2 x Z_2 A new class of codes over Z_2 x Z_2

2010-08-11

arxiv.org/abs/1008.1927v1

Mathematics

Combinatorics

LaTeX, 29 pages, 7 tables

Scientific paper

We study a new class of codes over Z_2 x Z_2 which we call L-codes. They arise as a natural fifth step in a series of analogies between Kleinian codes, binary codes, lattices and vertex operator algebras. This analogy will be explained in detail. We classify self-dual L-codes up to length 10 and provide tables for these codes and their weight enumerators up to length 4. We also discuss extremal codes for which a nearly complete classification is obtained.

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