Some Results in the Ring

Dr. Ranjeet Singh

doi:https://doi.org/10.14445/22315373/IJMTT-V35P505

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 35 | Number 1 | Year 2016 | Article Id. IJMTT-V35P505 | DOI : https://doi.org/10.14445/22315373/IJMTT-V35P505

Some Results in the Ring

Dr. Ranjeet Singh

Abstract

Let p, q and l be distinct odd primes and ( )[ ]/( 1) 2 2   n m n m p q p q R GF l x x .If n p o(l) = ( ) n  p /2, (n  1) and o(l)  (q )/ 2,(m 1) m q m  with gcd ( ( ) n  p /2, ( ) m  q /2) =1, then the explicit expressions for the complete set of 8mn+4n+4m+2 primitive idempotents in the ring ( )[ ]/( 1) 2 2   n m n m p q p q R GF l x x are obtained

Keywords

primitive idempotents; primitive root; irreducible quadratic residue cyclic codes; cyclotomic cosets.

References

[1] S.K.Arora, M.Pruthi, “Minimal Cyclic Codes of prime power length”, Finite Fields Appl.3 (1997)99-113.
[2] S.K. Arora, M. Pruthi, “Minimal Cyclic Codes of length 2pn” Finite Fields Appl. 5 (1999) 177-187.
[3] Anuradha Sharma, G.K.Bakshi, V.C. Dumir, M. Raka, “Cyclotomic Numbers and Primitive idempotents in the ring GF (l) [x]/< 1 pn x >”, Finite Fields Appl. 10 (2004) 653-673.
[4] G.K.Bakshi, Madhu Raka, “Minimal cyclic codes of length pnq”, Finite Fields Appl. 9 (2003) 432-448.
[5] Ranjeet Singh, M.Pruthi, “Irreducible Quadratic Residue Cyclic Codes of Length 2pnq (n 1)” Antarctica Journal of Mathematics vol.(7) 2010.

Citation :

Dr. Ranjeet Singh, "Some Results in the Ring," International Journal of Mathematics Trends and Technology (IJMTT), vol. 35, no. 1, pp. 32-37, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V35P505