The study of linear and cyclic codes over some types of finite rings has enabled the development of highly efficient codes with optimal parameters. Due to the algebraic properties of these rings, error-correction algorithms can be well adapted to diverse noisy channels, enhancing real-time performance. Furthermore, by using ideals in polynomial rings, cyclic codes ensure that hardware implementation remains remarkably straightforward and fast. For these reasons, in this paper, we describe linear and cyclic codes over the rings of the form Rs,p= Z ₚ[u]/( f( u) /( u-s) ), where p is a prime number and f( u) = uᵖ-u, with s∈ \0,1,,p-1\.
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Flaut et al. (2026) studied this question.
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