AI 中文总结
研究有限链环\(Z4 + iZ4\)上循环码和常循环码，证明常循环码与循环码等价，给出获取单根常循环码生成元算法，通过格雷映射得到线性\(Z4\)码并展示新的最佳线性\(Z4\)码。
AI 中文摘要
本文研究有限链环\(R = Z4 + iZ4\)（其中\(i^2 = -1\)）上的循环码和常循环码。证明了\(R\)上所有常循环码都与循环码等价，给出获取\(R\)上所有单根常循环码生成元的算法。通过格雷映射从\(R\)上的常循环码得到线性\(Z4\)码，并展示了用此方法找到的新的最佳线性\(Z4\)码。
英文摘要
In this paper, we study cyclic and constacyclic codes over the finite chain ring R=Z4+iZ4, where i^2=-1. We prove that all constacyclic codes over R are equivalent to cyclic codes. An algorithm to obtain generators for all simple root constacyclic codes over R is presented. Using a Gray map we then obtain linear Z4 codes from constacyclic codes over R. We present new best linear Z4 codes found using this method.
