基于六阶分圆序列的循环码的构造

A Construction of Cyclic Code from Cyclotomic Sequence of Order Six

摘要: 循环码是线性码中的一类，在电子产品、数据传输技术、广播系统有着广泛的应用。由于他们有着高效的编码和解码算法，在计算机中也有着广泛的应用。本文中，首先构造了在上周期为素数n的六阶分圆序列，并且给出了序列的线性复杂度和极小多项式。利用此序列的极小多项式作为循环码的生成多项式，构造了上长度为n的循环码。

Abstract: Cyclic code is a subclass of linear codes and has a lot of applications in consumer electronics, data transmission technologies, broadcast systems, and computer applications as it has efficient encoding and decoding algorithms. In this paper, the cyclotomic sequence of order six is employed to construct a class of cyclic codes over with prime length, and in addition its linear complexity and minima polynomial are determined. The minimal polynomial is served as the generator polynomial of cyclic code and constructs the cyclic codes over with the length of n.