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On optimal ( Z 6 m × Z 6 n , 4 , 1 ) and ( Z 2 m × Z 18 n , 4 , 1 ) difference packings and their related codes
Journal of Combinatorial Designs ( IF 0.5 ) Pub Date : 2021-11-16 , DOI: 10.1002/jcd.21812
Jingyuan Chen 1 , Lijun Ji 2
Affiliation  

We give a direct construction of a ( Z p × G , { 0 } × G , 4 , 1 ) relative difference family for G { Z 6 × Z 6 , Z 2 × Z 18 , Z 6 × Z 18 , Z 2 × Z 54 } and every prime p 3 ( mod 4 ) with p > 3. These allow us to construct an optimal ( Z 6 m × Z 6 n , 4 , 1 ) difference packing and an optimal ( Z 2 m × Z 18 n , 4 , 1 ) difference packing for every pair of positive integers ( m , n ) . The corresponding optimal optical orthogonal signature pattern codes are also obtained.

中文翻译:

关于最优( Z 6 m × Z 6 n , 4 , 1 ) 和( Z 2 m × Z 18 n , 4 , 1 ) 差分包装及其相关代码

我们直接构造一个 ( Z p × G , { 0 } × G , 4 , 1 ) 相对差异族 G { Z 6 × Z 6 , Z 2 × Z 18 , Z 6 × Z 18 , Z 2 × Z 54 } 和每个素数 p 3 ( 模组 4 ) p > 3. 这些使我们能够构建一个最优 ( Z 6 × Z 6 n , 4 , 1 ) 差异包装和最优 ( Z 2 × Z 18 n , 4 , 1 ) 每对正整数的差分打包 ( , n ) . 还获得了相应的最优光学正交特征码。
更新日期:2021-12-08
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