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A new class of codes over Z_2 x Z_2

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.

preprint2010arXivOpen access
Julia GalstadGerald Hoehn
math.COmath.QA
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Julia GalstadGerald Hoehn

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