CORRELATION OF BINARY SEQUENCE FAMILIES DERIVED FROM THE MULTIPLICATIVE CHARACTERS OF FINITE FIELDS
In this paper, new constructions of the binary sequence families of period q - 1 with large family size and low correlation, derived from multiplicative characters of finite fields for odd prime powers, are proposed. For m >= 2, the maximum correlation magnitudes of new sequence families S-m are bounded by (2m - 2)root q + 2m + 2, and the family sizes of S-m are given by q - 1 for m = 2, 2(q - 1) - 1 for m = 3, (q(2) - 1)q(m-4/2) for m even, m > 2, and 2(q - 1)q(m-3/2) for m odd, m > 3. It is shown that the known binary Sidel'nikov-based sequence families are equivalent to the new constructions for the case m = 2.
correlation binary sequences multiplicative characters weil bound