Constacyclic Codes of Arbitrary Length over $F_{q}+uF_{q}+\cdots +u^{e-1}F_{q}$

Document Type : Research Paper

Authors

1 Department of Mathematics, College of Sciences, Shiraz University, Shiraz, Iran

2 Department of Mathematics, College of Sciences, Shiraz University, Shiraz, 71467-13565, Iran.

10.29252/as.2019.1355

Abstract

In this article, we shall study the structure of $(a+bu)-$constacyclic codes of arbitrary length over the ring
$R=F_{q}+uF_{q}+\cdots +u^{e-1}F_{q}$, where $u^{e}=0$, $q$ is a power of a prime number $p$ and $a,b$ are non-zero elements of $F_{q}$. Also we shall find a minimal spanning set for these codes.  %, and completely determine the structure of these codes. For a constacyclic code $C$ we shall determine its minimum Hamming distance with some properties of $Tor(C)$ as an $a-$constacyclic code over $F_{q}$.

Keywords

References

[1] T. G. K. Bakshi and M. Raka, A class of constacyclic codes over a nite eld, Finite Field Appl., 18(2012),
362-377.
[2] B. Chen, Y. Fan, L. Lin and H. Liu, Constacyclic codes over nite elds, Finite Field Appl., 18(2012),
1217-1231.
[3] H. Q. Dinh, Constacyclic codes of length ps over Fpm + uFpm, J. Algebra, 324(2010), 940-950.
[4] H. Q. Dinh and H. D. T. Nguyen, On some classes of Constacyclic codes over polynomial residue rings,
Advances in Math. of comm., 6(2)(2012), 175-191.
[5] K.Guenda and T. A. Gulliver, Repeated root Constacyclic codes of length mps over Fpr + uFpr + : : : +
ue−1Fpr , J. Algebra and its Appl., 14(1)(2015), 1450081(12 pages).
[6] S. Jitman and P. Udomkavanich, On the structure of constacyclic codes of length ps over Fpk + uFpk +
   + um−1Fpk , Int. J. Algebra, 4(11)(2010), 507-516.
[7] X.Kai, S. Zhu and P. Li, (1 + u) Constacyclic codes over Fp[u], J. Franklin Institute, 347(2010),
751-762.
[8] J. L. Massey, D. J. Costello and J. Justesen, Polynomial weights and code constructions, IEEE Trans.
Inform. Theory, 19(1)(1973), 101-1