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.
Highlights
Cyclic codes are an interesting type of linear codes and have applications in communication and storage systems due to their efficient encoding and decoding algorithms
Li presented several classes of cyclic codes using another class of two-prime Whiteman generalized cyclotomic sequences of order 4, and gave lower bounds on the nonzero minimum hamming weight of these cyclic codes [16]
We consider the cyclic codes over the finite field of order q GF(q) from another class of two-prime Whiteman generalized cyclotomic sequences of order 6, and present the generator polynomials of these cyclic codes
Summary
Cyclic codes are an interesting type of linear codes and have applications in communication and storage systems due to their efficient encoding and decoding algorithms. Li presented several classes of cyclic codes using another class of two-prime Whiteman generalized cyclotomic sequences of order 4, and gave lower bounds on the nonzero minimum hamming weight of these cyclic codes [16]. The two-prime sequence is employed to construct several classes of cyclic codes of order d(d > 0) over GF(q) and lower bounds on the minimum weight of these cyclic codes were developed in [7]. The cyclic code Cs generated by the minimal polynomial of sn is called the cyclic code defined by the sequence sn, which is a linear [n, k] code with k = deg(gcd(xn −1, Sn(x))). The generator polynomial g(x) of cyclic code Cs is equal to the minimal polynomial of the sequence sn, i.e., g(x) xn − 1 gcd(xn − 1, S n(x)). The polynomial S(x) in Equation (3) is exactly the generator polynomial of the sequence sn [4]
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
