论文标题
$ x^n-λ$及其应用
Self-reciprocal and self-conjugate-reciprocal irreducible factors of $x^n-λ$ and their applications
论文作者
论文摘要
在本文中，我们提出了一些必要和充分的条件，在这些条件下，不可约多项式是自我续签（SR）或自轭 - 重物（SCR）。通过这些特征，我们获得了$ x^n-λ$，$λ\ in \ bbb f_q^*$，超过$ \ bbb f_q $的SR和SCR不可约的因素的一些枚举公式，这只是Boripan {\ em et al}（2019）所提出的。我们还以一种简单而直接的方式来计算欧几里得和遗传学LCD constacyclic代码的数量，并在欧几里得和赫尔米亚人的自我偶像constacyclic代码上显示了一些众所周知的结果。
In this paper, we present some necessary and sufficient conditions under which an irreducible polynomial is self-reciprocal (SR) or self-conjugate-reciprocal (SCR). By these characterizations, we obtain some enumeration formulas of SR and SCR irreducible factors of $x^n-λ$, $λ\in \Bbb F_q^*$, over $\Bbb F_q$, which are just open questions posed by Boripan {\em et al} (2019). We also count the numbers of Euclidean and Hermitian LCD constacyclic codes and show some well-known results on Euclidean and Hermitian self-dual constacyclic codes in a simple and direct way.
