Combinatorial constructions for optimal two-dimensional optical orthogonal codes with $\lambda$ = 2

TL;DR

This paper presents new combinatorial methods to construct optimal two-dimensional optical orthogonal codes with specific parameters, highlighting cases where the Johnson bound is not attainable.

Contribution

It introduces novel combinatorial constructions and infinite families of optimal codes with weight 4 and lambda=2, expanding the known solutions in the field.

Findings

Many infinite families of optimal codes are constructed.

Optimal codes often do not reach the Johnson bound.

New combinatorial techniques are developed for code construction.

Abstract

In this paper, we are concerned about optimal two-dimensional optical orthogonal codes with $\lambda$ = 2. Some combinatorial constructions are presented and many infinite families of optimal two-dimensional optical orthogonal codes with weight 4 and $\lambda$ = 2 are obtained. Especially, we shall see that in many cases an optimal two-dimensional optical orthogonal code can not achieve the Johnson bound.