Note: Cyclically permutable representations of cyclic codes

Authors:
Derek H. Smith;Stephanie Perkins
Affiliations:
Division of Mathematics and Statistics, University of Glamorgan, Pontypridd, CF37 1DL Wales, UK;Division of Mathematics and Statistics, University of Glamorgan, Pontypridd, CF37 1DL Wales, UK
Venue:
Discrete Applied Mathematics
Year:
2008

Citing 5
Cited 1

On a class of cyclically permutable error-correcting codes

IEEE Transactions on Information Theory
Cyclically permutable error-correcting codes

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Constructions of binary constant-weight cyclic codes and cyclically permutable codes

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Constructions for optimal constant weight cyclically permutable codes and difference families

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New constructions of optimal cyclically permutable constant weight codes

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Abstract

Cyclically permutable codes have been studied for several applications involving synchronization, code-division multiple-access (CDMA) radio systems and optical CDMA. The usual emphasis is on finding constant weight cyclically permutable codes with the maximum number of codewords. In this paper the question of when a particular error-correcting code is equivalent (by permutation of the symbols) to a cyclically permutable code is addressed. The problem is introduced for simplex codes and a motivating example is given. In the final section it is shown that the construction technique may be applied in general to cyclic codes.