New families of optimal variable-weight optical orthogonal codes with high weights

Abstract

The optical orthogonal codes (OOCs) have been widely used as spreading codes in communication systems employing the unipolar transmission. They are classified into constant-weight OOCs (CW-OOCs) and variable-weight OOCs (VW-OOCs) according to the number of distinct Hamming weights which their codewords have. In this paper, we present a new generic construction of VW-OOCs of length (q - 1) N from a CW-OOC of length N, where q is a prime power and gcd(q - 1, N) = 1. As a result, three new families of optimal VW-OOCs with a maximum correlation value 1 are obtained. In particular, these families can have the codewords of high weights, while most of the previously known optimal VW-OOCs have only codewords of weight less than 8.