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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 Sm are bounded by (2m-2)q√+2m+2, and the family sizes of Sm are given by q-1 for m=2, 2(q-1)-1 for m=3, (q2-1)q for m even, m>2, and 2(q-1)q 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. © 2013 AIMS.

Correlation of binary sequence families derived from the multiplicative characters of finite fields