Extremal weight enumerators and ultraspherical polynomials
Discrete Mathematics
Enumerative Combinatorics: Volume 1
Enumerative Combinatorics: Volume 1
Binomial moments of the distance distribution: bounds and applications
IEEE Transactions on Information Theory
An improved upper bound on the minimum distance of doubly-even self-dual codes
IEEE Transactions on Information Theory
New asymptotic bounds for self-dual codes and lattices
IEEE Transactions on Information Theory
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For self-dual codes with all weights divisible by an integer greater than one, the minimum distance is bounded by the Mallows-Sloane upper bounds and by their improvements due to Krasikov-Litsyn and Rains. We obtain the improved upper bounds from short relations with constant coefficients on suitable binomial moments of the codes. In this approach, the Mallows-Sloane bounds are analogues of the Singleton bound and the improved bounds are analogues of the Plotkin bound.