A method for constructing inequivalent self-dual codes with applications to length 56
IEEE Transactions on Information Theory
Duadic codes and difference sets
Journal of Combinatorial Theory Series A
Designs and their codes
Classification of Hadamard matrices of order 24 and 28
Discrete Mathematics
The p-ranks of skew Hadamard designs
Journal of Combinatorial Theory Series A
Quadratic double circulant codes over fields
Journal of Combinatorial Theory Series A
Self-Orthogonal 3-(56,12,65) Designs and Extremal Doubly-Even Self-Dual Codes of Length 56
Designs, Codes and Cryptography
On self-dual codes over $${\mathbb{F}}_5$$
Designs, Codes and Cryptography
Self-dual Codes over Small Prime Fields from Combinatorial Designs
CAI '09 Proceedings of the 3rd International Conference on Algebraic Informatics
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Skew Hadamard designs (4n --- 1, 2n --- 1, n --- 1) are associated to order 4n skew Hadamard matrices in the natural way. We study the codes spanned by their incidence matrices A and by I + A and show that they are self-dual after extension (resp. extension and augmentation) over fields of characteristic dividing n. Quadratic Residues codes are obtained in the case of the Paley matrix. Results on the p-rank of skew Hadamard designs are rederived in that way. Codes from skew Hadamard designs are classified. An optimal self-dual code over GF(5) is rediscovered in length 20. Six new inequivalent [56, 28, 16] self-dual codes over GF(7) are obtained from skew Hadamard matrices of order 56, improving the only known quadratic double circulant code of length 56 over GF(7).