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Expressions of Primitive Idempotents of Some Cyclic Codes of Length 16pn
Abstract
In the present paper, explicit expressions for primitive idempotent in group algebra of cyclic group G of length 16pn, where ‘p’ is prime and ‘q’ is prime or some prime power (of type 16k+13), ‘n’ is a positive integer, order of ‘q’ modulo pn is , are obtained. Associated with this the generating polynomial and minimum distance bounds for the corresponding cyclic codes are derived.In the present paper, explicit expressions for primitive idempotent in group algebra of cyclic group G of length 16pn, where ‘p’ is prime and ‘q’ is prime or some prime power (of type 16k+13), ‘n’ is a positive integer, order of ‘q’ modulo pn is , are obtained. Associated with this the generating polynomial and minimum distance bounds for the corresponding cyclic codes are derived.
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References

1. A. Sahni and P.T. Sehgal; Minimal Cyclic Codes of Length pnq. Finite Fields and Their Applications, 18(5), 1017-1036 (2012).
2. F. Li; Q. Yue and C. Li; Irrducible Cyclic Codes of Length 4pn and 8pn. Fields and Their Applications, 34, 208-234 (2015).
3. G.K. Bakshi and M. Raka; Minimal Cyclic Codes of Length pnq. Fields and Their Applications, 9(4), 432-448 (2003).
4. J. Singh and S.K. Arora; Minimal Cyclic Codes of Length 8pn Over GF(q), where q is Prime Power of the Form 8k+5. Journal of Applied Mathematics and Computing, 48(1-2), 55-69 (2015).
5. J. Singh; S.K. Arora and S. Chawla; Some Cyclic Codes of Length 8pn. International Journal of Pure and Applied Mathematics, 116(1), 217-241 (2017).
6. M. Pruthi and S.K. Arora; Minimal Codes of Prime Power Length. Fields and Their Applications, 3(2), 99-113 (1997).
7. S. Batra and S.K. Arora; Minimal Quadratic Cyclic Codes of Length pn (p Odd Prime). The Korean Journal of Computational & Applied Mathematics, 8(3), 531-547 (2001).
8. S. Batra and S.K. Arora; Some Cyclic Codes of Length 2pn.  Designs, Codes and Cryptography, 61(1), 41-69 (2011).
9. S.K. Arora and M. Pruthi; Minimal Cyclic Codes of Length 2pn. Fields and Their Applications, 5(2), 177-187 (1999).
10. S.K. Arora; S. Batra; S.D. Cohen and M. Pruthi; The Primitive Idempotents of a Cyclic Group Algebra. Southeast Assian Bulletin of Mathematics, 26(4), 549-557 (2002).
11. V. Pless, Introduction of the Theory of Error Correcting Codes. John Wiley & Sons, Inc., New York, 1981.

ISSN(P) 2350-0174

ISSN(O) 2456-2378

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