A correction to: on the linear complexity of the Sidelnikov–Lempel–Cohn–Eastman sequences
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In the paper of Kyureghyan and Pott (Des Codes Cryptogr 29:149–164, 2003), the linear feedback polynomials of the Sidelnikov–Lempel–Cohn–Eastman sequences were determined for some special cases. We found that Corollary 4 and Theorem 2 of that paper are wrong because there exist counterexamples for these two results. In this note, we give some counterexamples of Corollary 4 and Theorem 2, and correct them by readopting the negation of the condition of Lemma 5 as their necessary and sufficient conditions.
KeywordsLinear feedback polynomial Linear complexity The Sidelnikov–Lempel–Cohn–Eastman sequences Jacobsthal sums
Mathematics Subject Classification94A55
The authors of the present corrigendum thank very much the anonymous reviewer and the editor for their valuable comments and analysis. Minglong Qi was supported by the Foundation for the project Middleware Technologies of the Wuhan University of Technology under Grant 2012037. Shengwu Xiong was supported by the Foundation for the project Formation Model for Engineers in Software Engineering of Hubei Province under Grant 2012103.
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