Explicit factorization of a $(P,Q)$-circulant matrix-functions

The paper considers a factorization problem of a matrix-function, obtained from a circulant by a right and left multiplication by diagonal rational matrix-functions. Formulas for partial indices are obtained by means of ranks of a finite number of explicit type matrices. A factorization construction of this matrix-function based on factorization of finite number of functions is given as well.