On a Theorem of Kyureghyan and Pott

TL;DR

This paper identifies errors in previous results on the linear feedback polynomials of Sidel'nikov-Lempel-Cohn-Eastman sequences, providing counterexamples to correct the record.

Contribution

It corrects and clarifies the inaccuracies in Kyureghyan and Pott's earlier work by presenting counterexamples to their corollary and theorem.

Findings

Counterexamples disprove Corollary 4 and Theorem 2

Previous results are incorrect in certain cases

Clarification of the sequence properties

Abstract

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.