论文标题
自dual 2-quasi-cyclic代码和二面代码
Self-dual 2-quasi-cyclic Codes and Dihedral Codes
论文作者
论文摘要
我们表征了所谓的Goursat引理在有限的场F上的2 Quasi-cyclic代码的结构。通过表征，我们为2 QuaSi-Cyclic代码作为二面代码表现出必要且充分的条件。我们为自dual 2-quasi-cyclic代码（如果Charf = 2）或consta-diheDral代码（如果Charf Odd）获得了必要且充分的条件。结果，一个元素生成的任何自偶联的2 Quasi-cyclic代码都必须是（consta-）二二二二二二进制代码。特别是，任何自动双重循环代码都必须是（consta-）二面的。同样，我们表明了必要且充分的条件，即三个类（自偶双循环代码，自偶会2- Quasi-cyclic代码和自偶（consta-）二面代码）相互重合。
We characterize the structure of 2-quasi-cyclic codes over a finite field F by the so-called Goursat Lemma. With the characterization, we exhibit a necessary and sufficient condition for a 2-quasi-cyclic code being a dihedral code. And we obtain a necessary and sufficient condition for a self-dual 2-quasi-cyclic code being a dihedral code (if charF = 2), or a consta-dihedral code (if charF odd). As a consequence, any self-dual 2-quasi-cyclic code generated by one element must be (consta-)dihedral. In particular, any self-dual double circulant code must be (consta-)dihedral. Also, we show a necessary and sufficient condition that the three classes (the self-dual double circulant codes, the self-dual 2-quasi-cyclic codes, and the self-dual (consta-)dihedral codes) are coincide each other.
