Hamming and Symbol-Pair Distances of Repeated-Root Constacyclic Codes of Prime Power Lengths Over $\mathbb F_{p^m}+u\mathbb F_{p^m}$

The ring R = Fp ^m + uFp ^m has precisely p ^m (p ^m -1) units which are of the forms γ and α + uβ, where 0 ≠ α, β, γ ϵ Fp ^m . Using generator polynomial structures of constacyclic codes of length p ^s over R, the Hamming and symbol pair distance distributions of all such codes are completely determined. As examples, we provide some good codes with better parameters than the known ones