Constructions of families with unequal autoand cross-correlation constraints

Yang and Fuja presented constructions of codes with unequal correlation constraints (lambda_c < lambda_a). And specifically they have constructions for the case where lambda_a = 2 > lambda_c = 1. In their work they argue that it is important to make the cross-correlation (lambda_c) as small as possible, and not necessarily lambda_a = lambda_c. In this work we present a method to generate new Yang-Fuja type families with correlation constraints where lambda_c < lambda_a. We presented a method to increase the size of a family of a double periodic sequence with optical orthogonal code (OOC) length n = mp where m = p - 1, and p is a prime. In this work we present a new method that increases the size of a family of double periodic sequences without the restriction on m, we present a method to increase the weight of a double periodic array, and then combine both methods to produce Yang-Fuja type families of double periodic arrays with lambda_c < lambda_a. One of our main results is a theorem (Theorem 3, Section IV) that estimates lambda_c. With this theorem we obtain two new constructions of optical orthogonal codes with lambda_c < lambda_a.