New Families of Binary Sequences with Low Correlation and Large Size
In this paper, for odd n and any k with god(n, k) = 1, new binary sequence families S(k) of period 2(n)-1 are constructed. These families have maximum correlation 1-2(n+3/2), family size 2(2n) + 2(n) + 1 and maximum linear span n(n+1)/2. The correlation distribution of S(k) is completely determined as well. Compared with the modified Gold codes with the same family size, the proposed families have the same period and correlation properties, but larger linear span. As good candidates kith low correlation and large family size, the new families contain the Gold sequences and the Gold-like sequences. Furthermore, S(k) includes a subfamily S(1)(k) which has the same period, correlation distribution, family size and linear span as the family S(0)(2) recently constructed by Yu and Gong. In particular, when k = 1, S(1)(k) is exactly S(0)(2).
binary sequence low correlation linear span large family size periodic correlation quadratic form