Let $mathbb{F}_q$ be a finite field of q elements, $R=mathbb{F}_q+umathbb{F}_q$ (u2=0) and D2n= be a dihedral group of order n. Left ideals of the group ring R[D2n] are called left dihedral codes over R of length 2n, and abbreviated as left D2n-codes over R. Let n be a positive factor of qe+1 for some positive integer e. In this paper, any left D2n-code over R is uniquely decomposed into a direct sum of concatenated codes with inner codes Ai and outer codes Ci, where Ai is a cyclic code over R of length n and Ci is a linear code of length 2 over a Galois extension ring of R. More precisely, a generator matrix for each outer code Ci is given. Moreover, a formula to count the number of these codes is obtained, the dual code for each left D2n-code is determined and all self-dual left D2n-codes over R are presented, respectively.

Let Fq be a finite field of cardinality q, R=Fq[u]/=Fq+uFq+u2Fq+u3Fq (u4=0) which is a finite chain ring, and n be a positive integer satisfying gcd(q,n)=1. For any $delta,alphain mathbb{F}_{q}^{ imes}$, an explicit representation for all distinct (δ+αu2)-constacyclic codes over R of length n is given, and the dual code for each of these codes is determined. For the case of q=2m and δ=1, all self-dual (1+αu2)-constacyclic codes over R of odd length n are provided.