On Decimations of M-Sequences Giving Few Valued Cross-Correlations


Boztaş S., Özbudak F., Kurtaran Özbudak E., Tekin E.

The 11th International Workshop on Signal Design and its Applications in Communications (IWSDA'25), Sydney, Australia, 7 - 11 December 2025, pp.1-4, (Full Text)

  • Publication Type: Conference Paper / Full Text
  • Doi Number: 10.1109/iwsda67899.2025.11457433
  • City: Sydney
  • Country: Australia
  • Page Numbers: pp.1-4
  • TED University Affiliated: Yes

Abstract

In this paper, we report some experimental results on decimations d which yield three-valued cross-correlations for m - sequences over odd prime fields p. First, we performed a search for decimations different from the ones mentioned by Helleseth in his 2014 survey [6] of open problems on crosscorrelation. We have performed extensive computations but have not found any cases that are inequivalent to those stated as Open Problem 2 in [6]. In this context, we conjecture the form of the decimations that result in these three-valued crosscorrelations and leave the proof as an open problem. We also report computational results on a class of sequences related to Open Problem 8 from Helleseth and Li's [7] 2024 paper. Specifically, we investigate the case n2(mod4), which was explicitly excluded from the original problem. Based on our findings, we propose a new conjecture on the correlation distribution for this particular family, thus formulating a new, related open problem.