Abstract
Let Fq be a finite field with q elements and n=l1m1l2m2, m1≥1, m2≥1, where l1, l2 are distinct primes and l1l2|q−1. In this paper, we give all irreducible factors of xl1m1l2m2−1 over Fq and all primitive idempotents in a ring Fq[x]/〈xl1m1l2m2−1〉. Furthermore, we obtain the dimensions and the minimum Hamming distances of all irreducible cyclic codes of length l1m1l2m2 over Fq.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.