A new binary sequence family with low correlation and large size

For odd n=2l+1 and an integer ρ with 1≤ρ≤l, a new family S_o(ρ) of binary sequences of period 2ⁿ-1 is constructed. For a given ρ, S_o(ρ) has maximum correlation 1+2^n+2ρ-12/, family size 2^nρ, and maximum linear span n(n+1)/2. Similarly, a new family of S_e(ρ) of binary sequences of period 2ⁿ-1 is also presented for even n=2l and an integer ρ with 1≤ρn2+ρ/,2^nρ, and n(n+1)/2, respectively. The new family S_o(ρ) (or S_e(ρ)) 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_o(2) is discussed in detail by analyzing its distribution of correlation values.