Cyclic and Constacyclic Codes for F<sub>2</sub>[u,v]/<u<sup>2</sup>,v<sup>3</sup> – v,uv,vu>

Authors

  • TH. Rojita Chanu
  • ST. Timothy Kom
  • O. Ratnabala Devi

DOI:

https://doi.org/10.18311/jims/2022/30791

Keywords:

Cyclic Code, Constacyclic Code, Gray Map.

Abstract

In this paper, we study cyclic and β-constacyclic codes over the ?nite commutative ring R = F2[u,v]/<u2,v3 ? v,uv,vu> with ? = (1+u),(1+u+v+v2) and (1+v+v2). We establish a Gray map from R to F42 and prove that the Gray image of a cyclic code is a quasi-cyclic code of index 4. It is also shown that the Gray image of β-constacyclic code overRis either β-equivalent, β-equivalent or β-equivalent to a quasi-cyclic code of length 4n and index 4 over F2 when ? = (1 + u),(1 + u + v + v2) and (1 + v + v2), respectively.

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Published

2022-08-23

How to Cite

Rojita Chanu, T., Timothy Kom, S., & Ratnabala Devi, O. (2022). Cyclic and Constacyclic Codes for F<sub>2</sub>[u,v]/<u<sup>2</sup>,v<sup>3</sup> – v,uv,vu>. The Journal of the Indian Mathematical Society, 89(3-4), 279–291. https://doi.org/10.18311/jims/2022/30791