Handbook of Coding Theory
The Structure of 1-Generator Quasi-Twisted Codes and New Linear Codes
Designs, Codes and Cryptography
Pseudocyclic maximum-distance-separable codes
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Cyclic and negacyclic codes over finite chain rings
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
New MDS self-dual codes over finite fields
Designs, Codes and Cryptography
Trace representation of quasi-negacyclic codes
BICS'13 Proceedings of the 6th international conference on Advances in Brain Inspired Cognitive Systems
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This paper extends the concepts from cyclic duadic codes to negacyclic codes over F"q (q an odd prime power) of oddly even length. Generalizations of defining sets, multipliers, splittings, even-like and odd-like codes are given. Necessary and sufficient conditions are given for the existence of self-dual negacyclic codes over F"q and the existence of splittings of 2N, where N is odd. Other negacyclic codes can be extended by two coordinates in a way to create self-dual codes with familiar parameters.