Support weight distribution of linear codes
Discrete Mathematics - A collection of contributions in honour of Jack van Lint
Algorithms in invariant theory
Algorithms in invariant theory
Geometric approach to higher weights
IEEE Transactions on Information Theory - Part 1
Extremal binary self-dual codes
IEEE Transactions on Information Theory
Higher Weights for Ternary and Quaternary Self-Dual Codes*
Designs, Codes and Cryptography
On Higher Weights and Code Existence
Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
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The theory of higher weights is applied to binary self-dual codes. Bounds are given for the second minimum higher weight and a Gleason-type theorem is derived for the second higher weight enumerator. The second weight enumerator is shown to be unique for the putative [72, 36, 16] Type II code and the first three minimum weights are computed for optimal codes of length less than 32. We also determine the structures of the graded rings associated with the code polynomials of higher weights for small genera, one of which has the property that it is not Cohen-Macaulay.