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

Abstract

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.