On Decimations of M-Sequences Giving Few Valued Cross-Correlations
11th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2025, Melbourne, Avustralya, 7 - 11 Aralık 2025, (Tam Metin Bildiri)
- Yayın Türü: Bildiri / Tam Metin Bildiri
- Doi Numarası: 10.1109/iwsda67899.2025.11457433
- Basıldığı Şehir: Melbourne
- Basıldığı Ülke: Avustralya
- Anahtar Kelimeler: CDMA, correlation, sequence design, wireless communications
- TED Üniversitesi Adresli: Evet
Özet
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(mod 4), 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.