On Fpᵐ R-additive skew negacyclic codes

Let R = Fp^m + uFp^m with u^2 = 0 , where p is an odd prime and m is any positive integer. This article delves into the algebraic structure of skew negacyclic codes of length 2p^s over a finite field Fp^m and a finite chain ring R . The focus is on the classification and structural properties of these codes. Based on the different possible factorizations of x2p^s + 1 over Fp^m , a complete classification of the structural properties of skew negacyclic codes and their duals for length 2p^s over Fp^m and R is provided. Furthermore, the algebraic structure of Fp^mR -additive skew negacyclic codes with block length (p^s, 2p^s) is discussed. The separability of Fp^mR -additive skew negacyclic codes is also analyzed. To illustrate these results, several examples are presented, including the construction of Maximum Distance Separable (MDS) and near-MDS codes.