Cyclic codes from the first class two-prime Whiteman's generalized cyclotomic sequence with order 6

Pramod Kumar Kewat; Priti Kumari

doi:10.4134/BKMS.b170594

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2019; 56(2): 285-301

Online first article March 11, 2019 Printed March 1, 2019

https://doi.org/10.4134/BKMS.b170594

Cyclic codes from the first class two-prime Whiteman's generalized cyclotomic sequence with order 6

Pramod Kumar Kewat, Priti Kumari

Indian Institute of Technology (Indian School of Mines); Indian Institute of Technology (Indian School of Mines)

Abstract

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Abstract

Let $p_1$ and $p_2$ be two distinct odd primes with $\mathrm{gcd}(p_1-1,p_2-1)=6$. In this paper, we compute the linear complexity of the first class two-prime Whiteman's generalized cyclotomic sequence (WGCS-I) of order $d=6$. Our results show that their linear complexity is quite good. So, the sequence can be used in many domains such as cryptography and coding theory. This article enrich a method to construct several classes of cyclic codes over $\mathrm{GF}(q)$ with length $n=p_1p_2$ using the two-prime WGCS-I of order 6. We also obtain the lower bounds on the minimum distance of these cyclic codes.

Keywords: cyclic codes, finite fields, cyclotomic sequences

MSC numbers: 94A05, 94A55, 94B15