The Depth Distribution of Constacyclic Codes Over $F_p+vF_p$

The depth distribution of a linear code was put forward by Etzion as a new characterization for linear codes. The previously known results pay close attention to the depth distribution of the linear codes over chain rings. In this paper, we completely determine the depth spectrum and depth distribution of constacyclic codes over a non-chain ring F
_p
+ vF
_p
. For this purpose, we first investigate the depth spectrum of constacyclic codes over the finite field Fp. The corresponding result can be regarded as a generalization of [6, Th. 3], in the sense that we do not assume (n, p) = 1.