Polynomial Splitting Ring and Root Representation of Linear Recurring Sequences Over Z|(p~e)
Qi Wen · 1994
The concept of the splitting ring of the polynomial over ring Z(pe) is introduced and the factomation of polynomials and the properties df polynomial roots are discussed. By using these results and the structure of sequence families, it is shown that the terms of a linear recurring sequence over Z/(pe) may be represented by the roots of its characteristic polynomial and the representation is uniquely determined by the sequence.