On a Theorem of Kyureghyan and Pott
This is an incremental correction for researchers in coding theory and cryptography, addressing specific inaccuracies in prior results.
The paper identifies errors in a previous work by Kyureghyan and Pott, specifically finding counterexamples to Corollary 4 and Theorem 2 related to linear feedback polynomials of Sidel'nikov-Lempel-Cohn-Eastman sequences.
In the paper of Gohar M. Kyureghyan and Alexander Pott (Designs, Codes and Cryptography, 29, 149-164, 2003), the linear feedback polynomials of the Sidel'nikov-Lempel-Cohn-Eastman sequences were determined for some special cases. When referring to that paper, we found that Corollary 4 and Theorem 2 of that paper are wrong because there exist many counterexamples for these two results. In this note, we give some counterexamples of Corollary 4 and Theorem 2 of that paper.