Polycyclic codes over R

Document Type : Original paper

Author

Presidency University, Bangalore, Karnatakka-560064, India

Abstract

In this paper, we  discuss the structure of polycyclic codes over the ring $R=\mathbb{F}_q+u\mathbb{F}_q+v\mathbb{F}_q;u^2=\alpha u,v^2=v$ and $uv=vu=0$, where $\alpha$ is an unit element in $R.$ We introduce annihilator self-dual codes, annihilator self-orthogonal codes and annihilator LCD codes over R. Using a Gray map, we define a one to one correspondence between $R$ and $\mathbb{F}_q$ and  construct quasi polycyclic  codes over the  $\mathbb{F}_q$.

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References

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Communications in Combinatorics and Optimization
Volume 10, Issue 2
June 2025
Pages 371-379

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