Cyclic Codes from Two-Prime Generalized Cyclotomic Sequences of Order 6

TL;DR

This paper constructs new cyclic codes over finite fields using two-prime generalized cyclotomic sequences of order 6, providing generator polynomials and bounds on minimum distances, with applications in data storage and communication.

Contribution

It introduces a novel method for constructing cyclic codes from two-prime generalized cyclotomic sequences of order 6, including explicit generator polynomials and minimum distance bounds.

Findings

Constructed several classes of cyclic codes over GF(q).

Derived generator polynomials for these codes.

Provided lower bounds for the minimum distances.

Abstract

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