Second order Recurrences, quadratic number fields and cyclic codes

Mathematics > Number Theory [Submitted on 26 Mar 2026] Second order Recurrences, quadratic number fields and cyclic codes Minjia Shi, Xuan Wang, Bouazzaoui Zakariae, Jon-Lark Kim, Patrick Solé Wall-Sun-Sun primes (shortly WSS primes) are defined as those primes p such that the period of the Fibonacci recurrence is the same modulo p and modulo p^2. This concept has been generalized recently to certain second order recurrences whose characteristic polynomials admit as a zero the principal unit of \mathbb{Q}(\sqrt{d}), for some integer d>0. Primes of the latter type we call WSS(d). They correspond to the case when \mathbb{Q}(\sqrt{d}) is not p-rational. For such a prime p we study the weight distributions of the cyclic codes over \mathbb{F}_p and \mathbb{Z}_{p^2} whose check polynomial is the reciprocal of the said characteristic polynomial. Some of these codes are MDS (reducible case) or NMDS (irreducible case). Subjects: Number Theory (math.NT); Cryptography and Security (cs.CR) MSC classes: 11B39, 11B50, 11R11, 94B15 Cite as: arXiv:2603.25343 [math.NT]   (or arXiv:2603.25343v1 [math.NT] for this version)   https://doi.org/10.48550/arXiv.2603.25343 Focus to learn more Submission history From: Xuan Wang [view email] [v1] Thu, 26 Mar 2026 11:39:50 UTC (20 KB) Access Paper: HTML (experimental) view license Current browse context: math.NT < prev   |   next > new | recent | 2026-03 Change to browse by: cs cs.CR math References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)