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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.25343 |
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| _version_ | 1866915892574552064 |
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| author | Shi, Minjia Wang, Xuan Zakariae, Bouazzaoui Kim, Jon-Lark Solé, Patrick |
| author_facet | Shi, Minjia Wang, Xuan Zakariae, Bouazzaoui Kim, Jon-Lark Solé, Patrick |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25343 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Second order Recurrences, quadratic number fields and cyclic codes Shi, Minjia Wang, Xuan Zakariae, Bouazzaoui Kim, Jon-Lark Solé, Patrick Number Theory Cryptography and Security 11B39, 11B50, 11R11, 94B15 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). |
| title | Second order Recurrences, quadratic number fields and cyclic codes |
| topic | Number Theory Cryptography and Security 11B39, 11B50, 11R11, 94B15 |
| url | https://arxiv.org/abs/2603.25343 |