Self-dual codes over the integers modulo 4
Journal of Combinatorial Theory Series A
Designs, Codes and Cryptography
New Extremal Type II Codes Over Z_4
Designs, Codes and Cryptography
Type II Self-Dual Codes over Finite Rings and Even Unimodular Lattices
Journal of Algebraic Combinatorics: An International Journal
Euclidean and hermitian self-dual MDS codes over large finite fields
Journal of Combinatorial Theory Series A
Cyclic codes and quadratic residue codes over Z4
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Weight enumerators of self-dual codes
IEEE Transactions on Information Theory
The Z4-linearity of Kerdock, Preparata, Goethals, and related codes
IEEE Transactions on Information Theory
Quaternary quadratic residue codes and unimodular lattices
IEEE Transactions on Information Theory
Finite Fields and Their Applications
Construction of MDS self-dual codes over Galois rings
Designs, Codes and Cryptography
Self-dual codes using the building-up construction
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
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We present an efficient method for constructing self-dual or self-orthogonal codes over finite rings Z"p"^"m (or Z"m) with p an odd prime and m a positive integer. This is an extension of the previous work [J.-L. Kim, Y. Lee, Euclidean and Hermitian self-dual MDS codes over large finite fields, J. Combin. Theory Ser. A 105 (2004) 79-95] over large finite fields GF(p^m) to finite rings Z"p"^"m (or Z"m). Using this method we construct self-dual or self-orthogonal codes of length at least up to 10 over various finite rings Z"p"^"m or Z"p"q with q an odd prime, where p^m=25, 125, 169, 289 and pq=65, 85. All the self-dual codes we obtained are MDS, MDR, near MDS, or near MDR codes.