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. https://resolver.caltech.edu/CaltechAUTHORS:20170925-142327910

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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).

Item Type:

Article

Related URLs:

URL	URL Type	Description
https://doi.org/10.1109/TIT.2003.810623	DOI	Article
http://ieeexplore.ieee.org/document/1197853	Publisher	Article
https://arxiv.org/abs/math/0104145	arXiv	Discussion Paper

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:

DOI:

10.1109/TIT.2003.810623

Record Number:

CaltechAUTHORS:20170925-142327910

Persistent URL:

https://resolver.caltech.edu/CaltechAUTHORS:20170925-142327910

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: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1197853&isnumber=26952

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No commercial reproduction, distribution, display or performance rights in this work are provided.

ID Code:

81817

Collection:

CaltechAUTHORS

Deposited By:

Tony Diaz

Deposited On:

25 Sep 2017 21:37

Last Modified:

15 Nov 2021 19:46

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