The main objective of this paper is to extend the previously defined code family over the ring $\mathfrak{ R}=\sum\limits_{ s=0}^{ 4} v_{ 5}^{ s} \mathcal{ A}_{ 4}$ to $\mathfrak{ R}^{ s,m}=\sum\limits_{ \varsigma=1}^{ m} v_{ m}^{ \varsigma-1}\mathcal{ A}_{ m-1}$, and propose an expanded framework for its implementation in coding theory, and to derive additional properties from this generalized code family, including the construction of cyclic and quasi-cyclic codes. Furthermore, we will present specific applications of this extended code family.
Categories: cs.IT math.AC math.IT