Indian Journal of Pure and Applied Mathematics ( IF 0.7 ) Pub Date : 2021-07-01 , DOI: 10.1007/s13226-021-00001-2 Saroj Rani
Let p be an odd prime, and let m be a positive integer satisfying \(p^m \equiv 3~(\text {mod }4).\) Let \(\mathbb {F}_{p^m}\) be the finite field with \(p^m\) elements, and let \(R=\mathbb {F}_{p^m}[u]/\left\langle u^2\right\rangle\) be the finite commutative chain ring with unity. In this paper, we determine all constacyclic codes of length \(4p^s\) over R and their dual codes, where s is a positive integer. We also determine their sizes and list some isodual constacyclic codes of length \(4p^s\) over R.
中文翻译:
$${\mathbb{F}}_{p^m}[u]/\left\langle u^2\right\rangle$$ F pm [ u ] / u 2 上的一类恒环码
令p为奇素数,令m为满足\(p^m \equiv 3~(\text {mod }4).\)令\(\mathbb {F}_{p^m}\ )是具有\(p^m\)元素的有限域,并令\(R=\mathbb {F}_{p^m}[u]/\left\langle u^2\right\rangle\)为具有统一性的有限交换链环。在本文中,我们确定了R 上所有长度为\(4p^s\) 的恒循环码及其对偶码,其中s是一个正整数。我们还确定了它们的大小并在R 上列出了一些长度为\(4p^s\) 的等对恒环码。