The sizes of maximal \((v,k,k-2,k-1)\) optical orthogonal codes

An optical orthogonal code (OOC) is a family of binary sequences having good auto- and cross-correlation properties. Let \(\Phi (v,k,\lambda _{a},\lambda _{c})\) denote the largest possible size among all \((v,k,\lambda _{a},\lambda _{c})\)-OOCs. A \((v,k,\lambda _{a},\lambda _{c})\)-OOC with \(\Phi (v,k,\lambda _{a},\lambda _{c})\) codewords is said to be maximal. In this paper, we research into maximal \((v,k,k-2,k-1)\)-OOCs and determine the exact value of \(\Phi (v,k,k-2,k-1)\). This generalizes the result on the special case of \(k=4\) by Huang and Chang in 2012. Distributions of differences with maximum multiplicity are analyzed by several classes to deal with the general case for all possible v and k.