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Published May 2003 | Submitted + Published
Journal Article Open

New asymptotic bounds for self-dual codes and lattices

Abstract

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).

Additional Information

© 2003 IEEE. Manuscript received October 2, 2001; revised December 2, 2002. The author would like to thank H. Landau, A. M. Odlyzko, and N. J. A. Sloane for helpful discussions regarding Section II, especially Lemma 2.3, as well as I. Duursma for pointing out that I. Krasikov and S. Litsyn had improved their earlier bound to the one stated above.

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August 19, 2023
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