F[x]-lattice basis reduction algorithm and multisequence synthesis

Abstract

By means ofF[x]-lattice basis reduction algorithm, a new algorithm is presented for synthesizing minimum length linear feedback shift registers (or minimal polynomials) for the given multiple sequences over a fieldF. Its computational complexity isO(N 2) operations inF whereN is the length of each sequence. A necessary and sufficient condition for the uniqueness of minimal polynomials is given. The set and exact number of all minimal polynomials are also described whenF is a finite field.