The Linear Complexity of Binary Sequences With Optimal Autocorrelation

Binary sequences with optimal autocorrelation are needed in many applications. Two constructions of binary sequences with optimal autocorrelation of period N ≡ 0 (mod 4) are investigated. The two constructions are powerful and generic in the sense that many classes of binary sequences with optimal autocorrelation could be obtained from binary sequences with ideal autocorrelation. General results on the minimal polynomials of these binary sequences are derived. Based on the results, both the linear complexities and the minimal polynomials are determined.