GAUSS PERIODS AND CYCLIC CODES FROM CYCLOTOMIC SEQUENCES OF SMALL ORDERS

被引：1

作者：

Hu Liqin ^{[1
]}

Yue Qin ^{[1
]}

Zhu Xiaomeng ^{[1
]}

机构：

[1] Department of Mathematics, Nanjing University of Aeronautics and Astronautics

来源：

Journal of Electronics(China) | 2014年 / 31卷 / 06期

关键词：

Sequence; Cyclic code; Weight distribution; Gauss period; Cyclotomy;

D O I：

暂无

中图分类号：

O157.4 [编码理论（代数码理论）];

学科分类号：

070104 ;

摘要：

Let p =ef +1 be an odd prime with positive integers e and f. In this paper, we calculate the values of Gauss periods of order e =3, 4, 6 over a finite field GF(q), where q is a prime with q≠p. As applications, several cyclotomic sequences of order e =3, 4, 6 are employed to construct a number of classes of cyclic codes over GF(q) with prime length. Under certain conditions, the linear complexity and reciprocal minimal polynomials of cyclotomic sequences are calculated, and the lower bounds on the minimum distances of these cyclic codes are obtained.

引用

页码：537 / 546

页数：10

共 5 条

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