Families of shift-register sequences with impulsive correlation properties

A study of the linear feedback shift registers corresponding to a subset of nonprimitive irreducible polynomials over GF(2) has uncovered a class of sequences with interesting structures and cyclic correlation properties. These families of sequences are made up of interleaved identical sequences which are from primitive irreducible polynomials. Furthermore, they have correlation functions which are two or three valued, being constant at zero or a small value throughout most of their length with the exception of a small number of impulses. Each interval between such impulses on the correlograms uniquely corresponds to (and thus uniquely identifies) the member sequence or sequences producing it. It is shown that these families of sequences have direct application as error-correcting codes.