Doubly-Periodic Sequences and Two-Dimensional Recurrences
Steven Thomas Homer, Jerry Goldman · SIAM Journal on Algebraic and Discrete Methods · 1985
In this paper we study doubly-periodic sequences, which are a natural generalization of (singly) periodic sequences, a class which has proven to have wide-ranging applications. We present two-dimensional recurrence relations characterizing doubly-periodic sequences over finite rings and derive a number of properties of these double sequences using power series rings in two variables. Conditions for “factoring” such sequences as tensor products over fields are given and some results of Zierler on linear recurring sequences are extended. Applications are made to automata and product codes and conditions sufficient for a set of doubly periodic sequences to be a field with respect to certain operations are given.