标题： 新的自对偶码和格的渐近界 显示英文标题

标题： New asymptotic bounds for self-dual codes and lattices

摘要： 我们给出了Krasikov-Litsyn关于双偶自对偶二元码的d/n<~(1-5^{-1/4})/2界限的独立证明。所使用的技术（Mallows-Odlyzko-Sloane方法的改进）很容易扩展到其他自对偶码族、模格和量子码；特别是，我们证明了Krasikov-Litsyn界限适用于单偶二元码，并得到了一个类似界限用于单模格。我们还表明，在每种情况下，我们的界限与真实最优值之间的差异增长速度快于O(n^{1/2})。 显示英文摘要

摘要： 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}).