IEEE Transactions on Information Theory
Orthogonal Designs and Type II Codes over \Bbb{Z}_{2k}
Designs, Codes and Cryptography
On self-dual codes over some prime fields
Discrete Mathematics
Self-dual codes over Fp and weighing matrices
IEEE Transactions on Information Theory
Generalizations of Gleason's theorem on weight enumerators of self-dual codes
IEEE Transactions on Information Theory
Euclidean and hermitian self-dual MDS codes over large finite fields
Journal of Combinatorial Theory Series A
Self-Orthogonal and Self-Dual Codes Constructed via Combinatorial Designs and Diophantine Equations
Designs, Codes and Cryptography
MDS self-dual codes of lengths 16 and 18
International Journal of Information and Coding Theory
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Combinatorial designs have been used widely in the construction of self-dual codes. Recently a new method of constructing self-dual codes was established using orthogonal designs. This method has led to the construction of many new self-dual codes over small finite fields and rings. In this paper, we generalize this method by using generalized orthogonal designs, and we give another new method that creates and solves Diophantine equations over GF(p) in order to find suitable generator matrices for self-dual codes. We show that under the necessary conditions these methods can be applied as well to small and large fields. We apply these two methods to study self-dual codes over GF(31) and GF(37). Using these methods we obtain some new maximum distance separable self-dual codes of small orders.