On repeated-root constacyclic codes of length nps over 𝔽pm[u] 〈ua〉

Let [Formula: see text] be a prime number and [Formula: see text] finite field. Let [Formula: see text] be a finite chain ring, and let [Formula: see text], where [Formula: see text]. and [Formula: see text]. In this paper, we study [Formula: see text]-constacyclic codes of length [Formula: see text] over [Formula: see text], where [Formula: see text]. First, we use the Discrete Fourier Transform to decompose these codes via a ring isomorphism into direct sums of principal ideals. Using this decomposition, we explicitly determine the generator polynomials of such codes. We then study their duals and establish necessary and sufficient conditions for the existence of self-dual [Formula: see text]-constacyclic codes in the case where [Formula: see text]. Under this condition, we also provide their generator polynomials explicitly. Finally, we investigate the [Formula: see text]-symbol distances of these codes and derive explicit formulas. As an application, we generalize the results obtained in [6].