# Gauss periods and cyclic codes from cyclotomic sequences of small orders

Research paper by Liqin Hu, Qin Yue; Xiaomeng Zhu

Indexed on: 08 Aug '16Published on: 01 Dec '14Published in: Journal of Electronics (China)

#### Abstract

Abstract 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.AbstractLet 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.pefefeqqqpeq