Autocorrelation and linear complexity of binary generalized cyclotomic sequences with period \(pq\)
Summary: Ding constructed a new cyclotomic class \((V_0, V_1)\). Based on it, a construction of generalized cyclotomic binary sequences with period \(pq\) is described, and their autocorrelation value, linear complexity, and minimal polynomial are confirmed. The autocorrelation function \(C_S(w)\) is 3-level if \(p\equiv 3\mod 4\), and \(C_S(w)\) is 5-level if \(p\equiv 1\mod 4\). The linear complexity \(\text{LC}( S)>(pq,/,2)\) if \(p\equiv 1\mod 8\), \(p>q+1\), or \(p\equiv 3\mod 4\) or \(p\equiv -3\mod 8\). The results show that these sequences have quite good cryptographic properties in the aspect of autocorrelation and linear complexity.
scientific article; zbMATH DE number 7363793
scientific article