Codes Generated by Special Matrices on $ \mathbb{F}_2[u]/<u^3> $

Abstract

In this study, the results obtained by authors M. Ozkan and F. Oke [2] is extended the ring $ \mathbb{F}_2[u]/<u^3> $. Certain matrices lexicographically ordered are written using the elements of $ \mathbb{F}_2[u]/<u^3> $. The relations between the codes generated by these matrices and Hadamard codes are given.

Keywords

• Lexicographically ordered,Hadamard Codes,Codes over Ring

References

1. [1] Özkan, M. and Öke, F., On Codes written by matrices Lexicographically ordered, AIP Conf. Proceeding Vol:1926 (2018), 020035-1-020035-3.
2. [2] Özkan, M. and Öke, F., A relation between Hadamard codes and some special codes over F2 +uF2, App Mathematics and Inf. Sci. Vol:10, No:2 (2016), 701-704.
3. [3] Krotov, D. S., Z4-linear perfect codes, Diskretn. Anal. Issled. Oper. Ser.1 Vol:7, No:4 (2000), 78-90.
4. [4] Qian, J. , Zhang, L. and Zhu S., Constacyclic and cycliccodes over F2 +uF2 +u2F2, IEICE Trans. Fundamentals, E89-A, No: 6, (2006)1863-1865.
5. [5] Vermani, L. R., Elements of Algebraic Coding Theorytivity, Chapman Hall , India, 1996.
6. [6] Udomkavanich, P., Jitman, S., On the Gray Image of of ($1 - {u^m}$ )-Cyclic Codes ${\mathbb{F}_{p{\,^k}}}\, + \,u\,{\mathbb{F}_{p{\,^k}}} + ... + {u^m}{\mathbb{F}_{p{\,^k}}}$, Int. J. Contemp. Math. Sciences, Vol.26, No: 4, (2009)1265-1272.