Rotation-equivalence classes of binary vectors

Abstract

In this paper we study equivalence
classes of binary vectors with regards to their rotation
by using an algebraic approach based on the theory
of linear feedback shift registers. We state the necessary and
sufficient condition for existence of an equivalence class with
given cardinality and provide two formulas. The first represents
the sharp distribution of cardinalities for given length and
Hamming weight of binary vectors and the second enables us
to determine
the number of different classes with the same cardinality.