A new binary sequence family with low correlation and large size
For odd n = 2l + 1 and an integer rho with 1 <= rho <= l, a new family S-omicron(rho) of binary sequences of period 2(n)-1 is constructed. For a given rho, S-omicron(rho) has maximum correlation 1+2 n+2 rho-1/ 2, family size 2(n rho), and maximum linear-span n(n+1)/2. Similarly, a new family of S-omicron(rho) of binary sequences of period 2(n)-1 is also presented for even n = 2l and an integer rho with 1 <= rho < l, where maximum correlation, family size, and maximum linear span are 1 + 22/n+rho, 2(n rho), and n(n+1)/2 respectively. The new family S-omicron(rho) (or S-e(rho)) contains Boztas and Kumar's construction (or Udaya's) as a subset if m-sequences are excluded from both constructions. As a good candidate with low correlation and large family size, the family S-omicron(2) is discussed in detail by analyzing its distribution of correlation values.
linear span large family size family of binary sequences sequences with low correlation