A Note on the Games-Chan Algorithm

Abstract

The Games-Chan algorithm finds the minimal period of a periodic binary sequence of period $2^n$, in $n$ iterations. We generalise this to periodic $q$-ary sequences (where $q$ is a prime power) using generating functions and polynomials and apply this to find the multiplicity of $x-1$ in a $q$-ary polynomial $f$ in ${\log }_q°(f)$ iterations.

Exposition and main theorem improved, typos corrected. Application to finding multiplicity of x-1 in any $q$-ary polynomial added