The Berlekamp–Massey algorithm over commutative Artinian principal ideal rings

The algorithm constructing the monic polynomial of minimal degree which generates the given sequense of the length $l$ over commutative Artinian principal ideal ring $R$ is presented. The complexity of the algorithm is $O(l^2 n)$ operations of $R$, where $n$ is the index of nilpotency of the radical of $R$. The algorithm is applied for construction of the canonical system of generators of the ideal of all polynomials annihilating the given linear recurring sequence over $R$.