Volume 72 | Issue 8 | Year 2026 | Article Id. IJMTT-V72I8P102 | DOI : https://doi.org/10.14445/22315373/IJMTT-V72I8P102
Cyclotomic Cosets of Primitive Idempotents in Semi Simple Ring
| Received | Revised | Accepted | Published |
|---|---|---|---|
| 20 Jun 2026 | 23 Jul 2026 | 13 Aug 2026 | 29 Aug 2026 |
Ranjeet Singh, "Cyclotomic Cosets of Primitive Idempotents in Semi Simple Ring ," International Journal of Mathematics Trends and Technology (IJMTT), vol. 72, no. 8, pp. 8-10, 2026. Crossref, https://doi.org/10.14445/22315373/IJMTT-V72I8P102
We consider the ring where ๐,๐,๐ are distinct odd primes, l is a primitive root, both modulo
such that
.Explicit expressions for all the 16(๐ร๐ร๐+๐+๐+1) Cyclotomic Coset are obtained, ๐ does not divide qโ1 and ๐ is of the form 16k+1.
Cyclotomic Coset, Cyclic Codes, Minimal Cyclic Codes, Primitive Idempotent.
[1] Anuradha
Sharma et al., โCyclotomic Numbers and Primitive Idempotents in the Ring GF(q)
[x]/(
[CrossRef] [Google Scholar] [Publisher Link]
[2] Gurmeet
K. Bakshi, and Madhu Raka, โMinimal Cyclic Codes of Length pnq,โ
Finite Fields and Their Applications,
vol. 9, no. 4, pp. 432-448, 2003.
[CrossRef]
[Google Scholar] [Publisher Link]
[3] Amita
Sahni, and Poonam Trama Sehgal, โMinimal Cyclic Codes of Length pnq,โ
Finite Fields and Their Applications,
vol. 18, no. 5, pp. 1017-1036, 2012.
[CrossRef]
[Google Scholar] [Publisher Link]
[4] Gurmeet
Kaur Bakshi, Madhu Raka, and Anuradha Sharma, โIdempotent Generators of
Irreducible Cyclic Codes,โ Number Theory
& Discrete Geometry, vol. 6, pp. 13-18, 2008.
[Google Scholar]
[5] Ranjeet
Singh, and Manju Pruthi, โPrimitive Idempotents of Irreducible Quadratic
Residue Cyclic Codes of Length p^nq^m,โ International
Journal of Algebra, vol. 5, no. 5-8, pp. 285-294, 2011.
[Google Scholar] [Publisher Link]
[6] Florence
Jessie MacWilliams, and Neil James Alexander Sloane, The Theory of Error-Correcting Codes, vol. 16, Elsevier, 1977.
[Google Scholar]
[7] Vera
Pless, Introduction to the Theory of
Error-Correcting Codes, John Wiley & Sons, 1988.
[Google Scholar]
[8] George
Nemhauser, and Laurence Wolsey, Wiley-Interscience
Series in Discrete Mathematics and Optimization, Wiley, 1998.
[CrossRef]
[Google Scholar] [Publisher Link]
[9] Jagbir
Singh, and Sonika Ahlawat, โSome Cyclic Codes of Length 4pn and Their Minimum
Distance Bounds,โ International Journal
of Applied Engineering Research, vol. 13, no. 23, pp. 16708-16718, 2018.
[Publisher Link]
[10] Jagbir
Singh, and S.K. Arora, โMinimal Cyclic Codes of Length 8pn
over GF(q), where q is
Prime Power of the Form 8k +5,โ Journal of Applied Mathematics and Computing,
vol. 48, no. 1-2, pp. 55-69, 2014.
[CrossRef]
[Google Scholar] [Publisher Link]
[11] Jagbir
Singh, S.K. Arora, and Sheetal Chawla, โSome Cyclic Codes of Length 8pn,โ
International Journal of Pure and Applied
Mathematics, vol. 116, no. 1, pp. 217-241, 2017.
[CrossRef]
[Google Scholar]
[12] Ranjeet
Singh, โSome Cyclotomic Cosets in the Ring R_(8p^n q^m )=GF(l)[x] (x^(8p^n q^m
)-1),โ International Journal
of Advanced Research, vol. 14, no. 4, pp. 93-939, 2026.
[CrossRef]
[Publisher Link]