Some progress on optimal $ 2 $-D $ (n\times m,3,2,1) $-optical orthogonal codes

Abstract

In this paper, we are concerned about bounds and constructions of optimal 2-D (n × m, 3, 2, 1)-optical orthogonal codes. The exact number of codewords of an optimal 2-D (n × m, 3, 2, 1)-optical orthogonal code is determined for n = 2, m ≡ 1 (mod 2), and n ≡ 1 (mod 2), m ≡ 1, 3, 5 (mod 12), and n ≡ 4 (mod 6), m ≡ 8 (mod 16).