Cyclic codes from two-prime generalized cyclotomic sequences of order 6

Tongjiang Yan; Yanyan  Liu; Yuhua Sun

doi:10.3934/amc.2016036

Article Contents

2016, Volume 10, Issue 4: 707-723. Doi: 10.3934/amc.2016036

This issue Previous Article Note on the residue codes of self-dual $\mathbb{Z}_4$-codes having large minimum Lee weights Next Article Further results on semi-bent functions in polynomial form

Cyclic codes from two-prime generalized cyclotomic sequences of order 6

1.
College of Sciences, China University of Petroleum, 66 Changjiang Xilu, Qingdao, Shandong 266580
2.
College of Science, China University of Petroleum, Qingdao, Shandong 266580

Received: July 2014

Published: November 2016

Abstract / Introduction Related Papers Cited by

Abstract

Cyclic codes have wide applications in data storage systems and communication systems. Employing binary two-prime Whiteman generalized cyclotomic sequences of order 6, we construct several classes of cyclic codes over the finite field $\mathrm{GF}(q)$ and give their generator polynomials. And we also calculate the minimum distance of some cyclic codes and give lower bounds on the minimum distance for some other cyclic codes.

Keywords:

Cyclic codes,
Whiteman generalized cyclotomic sequences,
generator polynomial,
minimum distance.

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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