New asymptotic bounds for self-dual codes and lattices

Details New asymptotic bounds for self-dual codes and lattices New asymptotic bounds for self-dual codes and lattices

2001-04-12

arxiv.org/abs/math/0104145v1

Mathematics

Combinatorics

27 pages LaTeX, AMS macros

Scientific paper

We give an independent proof of the Krasikov-Litsyn bound d/n<~(1-5^{-1/4})/2 on doubly-even self-dual binary codes. The technique used (a refinement of the Mallows-Odlyzko-Sloane approach) extends easily to other families of self-dual codes, modular lattices, and quantum codes; in particular, we show that the Krasikov-Litsyn bound applies to singly-even binary codes, and obtain an analogous bound for unimodular lattices. We also show that in each case, our bound differs from the true optimum by an amount growing faster than O(n^{1/2}).

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