Research Information System
IEEE Access, vol.13, pp.135527-135537, 2025 (SCI-Expanded, Scopus)
This paper investigates the algebraic structure and properties of skew cyclic codes over the finite chain ring R = Z4 + uZ4, where u2 = 0. A central contribution of this work is the introduction and application of a novel Gray map, establishing a distance-preserving link between codes over R and linear codes over Z4.We employ a specific, compatible pair consisting of a ring automorphism θ and a θ-derivation η to define the appropriate skew polynomial ring structure R[x; θ, η]. Within this algebraic framework, we provide a comprehensive analysis of the fundamental structure of free (θ, η)-cyclic codes, detailing their generator polynomial structure and establishing their precise relationship with classical cyclic or quasi-cyclic codes. Furthermore, the structure of Euclidean dual codes for these free codes is examined for even lengths, and a construction for double (θ, η)-cyclic codes from free constituent codes is also presented.