On decimations of m-sequences giving few valued cross-correlations

Official URL: http://dx.doi.org/10.1109/IWSDA67899.2025.11457433

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 n≡2(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.