# Optimal optical orthogonal signature pattern codes with weight three and cross-correlation constraint one

## TL;DR

This paper establishes improved upper bounds and exact codeword counts for optimal optical orthogonal signature pattern codes with weight three and cross-correlation one, relevant for optical network communications.

## Contribution

It provides new upper bounds and exact codeword counts for specific classes of OOSPCs, advancing the theoretical understanding of their optimal design.

## Key findings

- Established an improved upper bound on code size.
- Determined the exact number of codewords for certain parameters.
- Applicable to optical network signature pattern design.

## Abstract

Optical orthogonal signature pattern codes (OOSPCs) have attracted wide attention as signature patterns of spatial optical code division multiple access networks. In this paper, an improved upper bound on the size of an $(m,n,3,\lambda_a,1)$-OOSPC with $\lambda_a=2,3$ is established. The exact number of codewords of an optimal $(m,n,3,\lambda_a,1)$-OOSPC is determined for any positive integers $m,n\equiv2\ ({\rm mod }\ 4)$ and $\lambda_a\in\{2,3\}$.