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Optimal 2-D (n × m, 3, 2,1)-optical orthogonal codes and related equi-difference conflict avoiding codes

机译:最佳的2-D(n×m,3,2,1) - 光学正交码及相关的Equi差异冲突避免代码

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摘要

This paper focuses on constructions for optimal 2-D (n x m, 3, 2, 1)-optical orthogonal codes with m equivalent to 0 (mod 4). An upper bound on the size of such codes is established. It relies heavily on the size of optimal equi-difference 1-D (m, 3, 2, 1)-optical orthogonal codes, which is closely related to optimal equi-difference conflict avoiding codes with weight 3. The exact number of codewords of an optimal 2-D (n x m, 3, 2, 1)-optical orthogonal code is determined for n = 1, 2, m = 0 (mod 4), and n = 0 (mod 3), m = 8 (mod 16) or m = 32 (mod 64) or m = 4, 20 (mod 48).
机译:本文侧重于具有M等于0(MOD 4)的最佳2-D(n x m,3,2,1)-optical正交码的结构。建立了这些代码大小的上限。它严重依赖于最佳Equi差异1-D(M,3,2,1) - 光正交码的大小,这与避免重量3的代码密切相关。码字的确切数量对于n = 1,2,m = 0(mod 4)确定最佳的2-d(nxm,3,2,1)-optical正交码,n = 0(mod 3),m = 8(mod 16 )或m = 32(mod 64)或m = 4,20(mod 48)。

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