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New asymptotic bounds for self-dual codes and lattices

Rains, Eric M. (2003) New asymptotic bounds for self-dual codes and lattices. IEEE Transactions on Information Theory, 49 (5). pp. 1261-1274. ISSN 0018-9448. doi:10.1109/TIT.2003.810623.

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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).

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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.
Subject Keywords:Asymptotic bounds, linear programming, modular lattices, saddle-point method, self-dual codes
Issue or Number:5
Record Number:CaltechAUTHORS:20170925-142327910
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Official Citation:E. M. Rains, "New asymptotic bounds for self-dual codes and lattices," in IEEE Transactions on Information Theory, vol. 49, no. 5, pp. 1261-1274, May 2003. doi: 10.1109/TIT.2003.810623 URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81817
Deposited By: Tony Diaz
Deposited On:25 Sep 2017 21:37
Last Modified:15 Nov 2021 19:46

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