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

TL;DR

This paper constructs new cyclic codes over finite fields using a specific type of cyclotomic sequence derived from two prime numbers, providing bounds on their minimum distances.

Contribution

It introduces a novel application of the second class two-prime Whiteman's generalized cyclotomic sequence of order 6 for cyclic code construction.

Findings

Constructed cyclic codes with specified lengths over GF(q)

Derived lower bounds on minimum distances of these codes

Expanded the use of cyclotomic sequences in coding theory

Abstract

Let $n_1=ef+1$ and $n_2=ef'+1$ be two distinct odd primes with positive integers $e,\ f,\ f'.$ In this paper, the two-prime Whiteman's generalized cyclotomic sequence of order $e=6$ is employed to construct several classes of cyclic codes over $\mathrm{GF}(q)$ with length $n_1n_2$. The lower bounds on the minimum distance of these cyclic codes are obtained.