Abstract
Cyclic codes are a subclass of linear codes and have wide applications in data storage systems, communication systems and consumer electronics due to their efficient encoding and decoding algorithms. Let p≥5 be an odd prime and m be a positive integer. Let C(1,e,s) denote the p-ary cyclic code with three nonzeros α, αe, and αs, where α is a generator of Fpm⁎, s=pm−12, and 2≤e≤pm−2. In this paper, by analyzing the solutions of certain equations over finite fields, we present four classes of optimal p-ary cyclic codes C(1,e,s) with parameters [pm−1,pm−2m−2,4]. Some known results on optimal quinary cyclic codes with parameters [5m−1,5m−2m−2,4] are special cases of our constructions. In addition, by analyzing the irreducible factors of certain polynomials over F5m, we present two classes of optimal quinary cyclic codes C(1,e,s).
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.
