Linear intersection pairs of linear codes have become of interest due to their nice algebraic properties and wide applications. In this paper, we focus on linear intersection pairs of cyclic codes over finite fields. Some properties of cyclotomic cosets in cyclic groups are presented as key tools in the study of such linear intersection pairs. Characterization and constructions of two cyclic codes of a fixed intersecting dimension are given in terms of their generator polynomials and cyclotomic cosets. In some cases, constructions of two cyclic codes of a fixed intersecting subcode are presented as well. Based on the theoretical characterization, some numerical examples of linear intersection pairs of cyclic codes with good parameters are illustrated.

翻译：线性码的线性交对因其良好的代数性质和广泛应用而受到关注。本文聚焦于有限域上循环码的线性交对。作为研究此类线性交对的关键工具，给出了循环群中分圆陪集的一些性质。基于生成多项式和分圆陪集，实现了具有固定交维数的两个循环码的刻画与构造。在某些情形下，还给出了具有固定交织子码的两个循环码的构造方法。基于理论刻画，本文展示了若干具有良好参数的循环码线性交对的数值实例。