Synthesis and uniqueness of m-sequences over GF(q/sup n/) as n-phase sequences over GF(q)

摘要

The construction of m-sequences over GF(q/sup n/) from known m-sequences over GF(q) is discussed. An algorithm is given which generates m-sequences over GF(q/sup n/) from m-sequences over GF(q), where n phase shifts of known m-sequences over GF(q) are determined by the iterative polynomials. It is shown that n shift distinct m-sequences over GF(q/sup n/) generated by the same m-sequences over GF(q) are unique when the elements of GF(q/sup n/) are represented by n-tuples of the elements from GF(q).