Linear Codes over ℜ^s,m=∑_ς=1^m v_m^ς-1𝒜_m-1, with v_m^m=v_m
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The main objective of this paper is to extend the previously defined code family over the ring ℜ=∑_s=0^4 v_5^s𝒜_4 to ℜ^s,m=∑_ς=1^m v_m^ς-1𝒜_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.
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