Open Access
Subscription Access
Open Access
Subscription Access
On Cyclic and Negacyclic Codes of Length 8ps Over Fpm + uFpm
Subscribe/Renew Journal
In this paper, we establish the algebraic structure of all cyclic and negacyclic codes of length 8ps over the chain ring Fpm + uFpm in terms of their generator polynomials, where u2 = 0 and s is a positive integer and p is an odd prime. We also find out the number of codewords in each of these cyclic codes. Besides this, we determine duals of cyclic codes and list self-dual cyclic and negacyclic codes of length 8ps over Fpm + uFpm. Also, we determine μ and -constacyclic codes of length 8ps over Fpm + uFpm.
Keywords
Cyclic Codes, Negacyclic Codes, Constacyclic Codes, Dual Codes, Self-dual Codes.
Subscription
Login to verify subscription
User
Font Size
Information
- E. R. Berlekamp, Algebraic Coding Theory, McGraw-Hill Book Company, New York, 1968.
- I. F. Blake, S. Gao and R. C. Mullin, Explicit factorization of X2k + 1 over Fp with prime p ≡ 3 (mod 4), App. Algebra Engrg. Comm. Comput., 4. (1993), 89–94.
- B. Chen, H. Q. Dinh, H. Liu and L. Wang, Constacyclic codes of length 2p s over Fpm + uFpm, Finite Fields Appl., 37. (2016), 108–130 .
- H. Q. Dinh, Constacyclic codes of length p s over Fpm + uFpm, J. Algebra, 324. (5) (2010), 940–950.
- H. Q. Dinh, On repeated-ischolar_main constacyclic codes of length 4ps , Asian-Eur. J. Math., 6. (2)(2013), DOI: 10.1142/S1793557113500204.
- H. Q. Dinh, S. Dhompongsa, and S. Sriboonchitta, On constacyclic codes of length 4ps over Fpm + uFpm, Discrete Math., 340. (2017), 832–849.
- H. Q. Dinh, Y. Fan, H. Liu, X. Liu and S. Sriboonchitta, On self-dual constacyclic codes of length ps over Fpm + uFpm, Discrete Math., 341. (2018), 324–335.
- H. Q. Dinh and S. R. Lopez-Permouth, Cyclic and negacyclic codes over finite chain rings, IEEE Trans. Inform. Theory, 50. (8) (2004), 1728–1744.
- H. Q. Dinh, B. T. Nguyen, S. Sriboonchitta and Thang M. Vo, On (α+uβ)-constacyclic codes of length 4ps over Fpm + uFpm, Journal of Algebra and its applications, 18.(2)(2019), DOI: 10.1142/S0219498819500233.
- H. Q. Dinh, A. Sharma, S. Rani and S. Sriboonchitta, Cyclic and negacyclic codes of length 4ps over Fpm + uFpm, Journal of Algebra and its applications, 17. (9) (2018), DOI: 10.1142/S0219498818501736.
- H. Q. Dinh, L. Wang and S. Zhu, Negacyclic codes of length 2ps over Fpm + uFpm, Finite Fields Appl., 31. (2015), 178–201.
- A. R. Hammons, Jr., P. V. Kumar, A. R. Calderbank, N. J. A. Sloane and P. Sole, The Z4-linearity of Kerdock, Preparata, Goethals and related codes, IEEE Trans. Inform. Theory, 40. (2) (1994), 301–319.
- V. Pless and Z. Qian, Cyclic codes and quadratic residue codes over Z4, IEEE Trans. Inform. Theory, 42. (5) (1996), 1594–1600 .
- V. Pless, P. Sole and Z. Qian, Cyclic self-dual Z4-codes, Finite Fields Appl., 3. (1) (1997), 48–69.
- E. Prange, Cyclic error-correcting codes in two symbols, Air Force Cambridge Research Labs, Bedford, Mass, TN-57-103 (1957).
- S. Rani, Constacyclic codes, PhD Thesis, IIT Delhi, available at http://eprint.iitd.ac.in/handle/12345678/7199.
Abstract Views: 606
PDF Views: 0