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A counter-example to a recent result on theq-ary image of aq s-ary cyclic code

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Abstract

We show, by means of a counter-example, that the necessary and sufficient conditions given in a recent paper [3] in order for theq-ary image of aq s-ary cyclic code to be cyclic are incorrect.

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References

  1. M. Hanan and F.P. Palermo, On cyclic codes for multi-phase data transmission systems,SIAM J. Appl. Math., Vol. 12, pp. 794–804, (1964).

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  2. F.J. MacWilliams, On binary cyclic codes which are also cyclic codes overGF(2s),SIAM J. Appl. Math., Vol. 19, pp. 75–95, (1970).

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  3. D.G. Leonard, Linear cyclic codes of wordlengthv overGF(q s) which are also cyclic codes of wordlengthsv overGF(q), Designs, Codes and Cryptography, Kluwer Academic Publishers, Vol. 1, pp. 183–189, (1991).

  4. G.E. Séguin, Theq-ary Image of aq m-ary Cyclic Code, presented at the 16th Biennial Symposium on Communications held at Queen's University, Kingston, Ontario, May 27–29, (1992).

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Royal Military College of Canada, K7K 5L0, Kingston, Ontario, Canada

    Gérald E. Séguin

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  1. Gérald E. Séguin
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Communicated by S. Vanstone

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Séguin, G.E. A counter-example to a recent result on theq-ary image of aq s-ary cyclic code. Des Codes Crypt 4, 171–175 (1994). https://doi.org/10.1007/BF01578870

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  • DOI: https://doi.org/10.1007/BF01578870

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