Let R = F㵯 + uF㵯 with u² = 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 2pˢ over a finite field F㵯 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 x^2pˢ + 1 over F㵯, a complete classification of the structural properties of skew negacyclic codes and their duals for length 2pˢ over F㵯 and R is provided. Furthermore, the algebraic structure of F㵯R -additive skew negacyclic codes with block length (pˢ, 2pˢ) is discussed. The separability of F㵯R -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.
Raj et al. (Wed,) studied this question.
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