Linear recursive sequences over Galois rings
Алексей Сергеевич Кузьмин, Alexander A. Nechaev · Russian Mathematical Surveys · 1993
Linear recurrences of maximal period over a Galois ring and over a residue class ring modulo p are studied. For any such recurrence, the coordinate sequences (in p-adic and some other expansions) are considered as linear recurring sequences over a finite field. Upper and lower bounds for the ranks (linear complexities) of these coordinate sequences are obtained. The results are based on using the properties of Galois rings and the trace-function on such rings.