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).

翻译：Wall-Sun-Sun素数（简称WSS素数）定义为满足斐波那契递归模$p$和模$p^2$周期相同的素数$p$。这一概念近年来被推广至某些二阶递归，其特征多项式以$\mathbb{Q}(\sqrt{d})$（其中$d>0$为整数）的主单位为零点。我们将后一类素数称为$WSS(d)$素数，它们对应于$\mathbb{Q}(\sqrt{d})$非$p$-有理的情形。对于此类素数$p$，我们研究了以该特征多项式的互反多项式为校验多项式的$\mathbb{F}_p$和$\mathbb{Z}_{p^2}$上循环码的重量分布。其中部分码为MDS（可约情形）或NMDS（不可约情形）。