Skew constacyclic codes over finite chain rings
Somphong Jitman, San Ling, Patanee Udomkavanich · Advances in Mathematics of Communications · 2012
Skew polynomial rings over finite fields and over Galois ringshave recently been used to study codes. In this paper, we extend this concept to finite chain rings.Properties of skew constacyclic codes generated by monic right divisors of $x^n-\lambda$, where $\lambda$ is aunit element, are exhibited. When $\lambda^2=1$, the generators of Euclidean and Hermitian dual codes of suchcodes are determined together with necessary and sufficient conditions for them to be Euclidean and Hermitian self-dual. Specializing to codes over the ring $\mathbb F$pm$+u\mathbb F$pm, the structure of allskew constacyclic codes is completely determined. This allows us to express the generators ofEuclidean and Hermitian dual codes of skew cyclic and skew negacyclic codes in terms of the generators of theoriginal codes. An illustration of all skew cyclic codes of length $2$ over $\mathbb F_3 + u\mathbb F_3$ andtheir Euclidean and Hermitian dual codes is also provided.