2010/08/02 by Somphong Jitman, Jitman, Somphong, San Ling +3 · 1 citation
Computer Science · #Coding theory and cryptography #Quantum-Dot Cellular Automata
paper · pdf · doi:10.48550/arxiv.1008.0327
Skew polynomial rings over finite fields ([7] and [10]) and over Galois rings ([8]) have 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 xn-λ, where λ is a unit element, are exhibited. When λ2=1, the generators of Euclidean and Hermitian dual codes of such codes are determined together with necessary and sufficient conditions for them to be Euclidean and Hermitian self-dual. Of more interest are codes over the ring \mathbbFpm+u\mathbbFpm. The structure of all skew constacyclic codes is completely determined. This allows us to express generators of Euclidean and Hermitian dual codes of skew cyclic and skew negacyclic codes in terms of the generators of the original codes. An illustration of all skew cyclic codes of length~2 over \mathbbF3+u\mathbbF3 and their Euclidean and Hermitian dual codes is also provided.