The University of Michigan Combinatorics Seminar
Abstract: We discuss some new bounds on the asympotic performance of self-dual codes and lattices. In the case of doubly-even self-dual binary codes, we recover the Krasikov-Litsyn bound d/n <~ (1-5-1/4)/2; however, our technique extends easily to other families of self-dual codes, modular lattices, and quantum codes. In particular, we show that the Krasikov-Litsyn bound applies without the restriction to doubly-even codes, and obtain a corresponding 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(n1/2).