Linear complexity of cyclotomic sequences of order six and BCH codes over GF(3)

Liqin Hu; Qin Yue; Fengmei Liu

doi:10.3934/amc.2014.8.297

Article Contents

2014, Volume 8, Issue 3: 297-312. Doi: 10.3934/amc.2014.8.297

This issue Previous Article On the dual code of points and generators on the Hermitian variety $\mathcal{H}(2n+1,q^{2})$ Next Article Construction of skew cyclic codes over $\mathbb F_q+v\mathbb F_q$

Linear complexity of cyclotomic sequences of order six and BCH codes over GF(3)

1.
Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016
2.
Science and Technology on Information Assurance Laboratory, Beijing, 100072

Received: April 2013

Revised: December 2013

Published online: August 2014

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Abstract

In this paper, we always assume that $p=6f+1$ is a prime. First, we calculate the values of exponential sums of cyclotomic classes of orders 3 and 6 over an extension field of GF(3). Then, we give a formula to compute the linear complexity of all $p^{n+1}$-periodic generalized cyclotomic sequences of order 6 over GF(3). After that, we compute the linear complexity and the minimal polynomial of a $p^{n+1}$-periodic, balanced and generalized cyclotomic sequence of order 6 over GF(3), which is analogous to a generalized Sidelnikov's sequence. At last, we give some BCH codes with prime length $p$ from cyclotomic sequences of orders three and six.

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Mathematics Subject Classification: Primary: 11T23; Secondary: 94A55, 94A60.

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