Downloads: 133
M.Tech / M.E / PhD Thesis | Mathematics | Kenya | Volume 6 Issue 4, April 2017
Enumeration of Cyclic Codes over GF(19)
Maganga Nyanchama Joash | Dr. Benard M. Kivunge
Abstract: In this paper we seek the number of irreducible polynomials of x^n-1 over GF (19). First, we factorize x^n-1 into irreducible polynomials over GF (19) using cyclotomic cosets of 19 modulo n. The number of irreducible polynomial factors of x^n-1 over GF (19) is equal to the number of cyclotomic cosets of 19 modulo n and each monic divisor of x^n-1 is a generator polynomial of a cyclic code in GF (19). Next, we show that the number of cyclic codes of length n over a finite field GF (19) is equal to the number of polynomials that divide x^n-1. Lastly, we enumerate the number of cyclic codes of length n, for 1n20 and when n=19k, n=19^k for 1k20
Keywords: Code, Cyclic Code, Cyclotomic cosets
Edition: Volume 6 Issue 4, April 2017,
Pages: 579 - 583
Similar Articles with Keyword 'Code'
Downloads: 185 | Weekly Hits: ⮙1 | Monthly Hits: ⮙1
Research Paper, Mathematics, China, Volume 9 Issue 7, July 2020
Pages: 1277 - 1281Different Numerous Systems Correspond to Different Universes: Revealing the Secret behind Nikola Tesla Code of 3, 6, 9
Downloads: 3 | Weekly Hits: ⮙2 | Monthly Hits: ⮙3
Research Paper, Mathematics, India, Volume 12 Issue 1, January 2023
Pages: 1305 - 1310