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Table 1 Distribution of cross-correlation values between the p members of two p × p arrays

From: Extended families of 2D arrays with near optimal auto and low cross-correlation

7 0.52 0.452 0.03 0 0 0        
11 0.432 0.488 0.08 0.002 0 0 0       
19 0.344 0.477 0.16 0.022 0 0 0 0      
23 0.316 0.464 0.18 0.036 0 0.0001 6E-06 0 0     
31 0.276 0.435 0.21 0.064 0.01 0.001 5E-05 9E-07 0     
43 0.236 0.396 0.24 0.098 0.03 0.005 0.0006 0.0001 0 0    
47 0.228 0.386 0.24 0.106 0.03 0.0075 0.0013 0.0001      
59 0.204 0.357 0.24 0.127 0.05 0.0154 0.0033 0.0005 0 0    
67 0.191 0.342 0.24 0.136 0.06 0.0211 0.0058 0.0012 2E-04 4E-05 5E-06   
71 0.186 0.334 0.24 0.14 0.06 0.0243 0.0071 0.0017 3E-04 0 0   
79 0.177 0.321 0.24 0.146 0.07 0.0301 0.01 0.0027 6E-04 0.00011 1E-05   
83 0.172 0.315 0.24 0.149 0.08 0.0337 0.0115 0.0034 0.008 0.00136 2E-04 2E-05  
103 0.155 0.289 0.23 0.157 0.09 0.0467 0.0201 0.0072 0.002 0.00061 1E-04 0.0002 1E-05
127 0.14 0.264 0.22 0.161 0.1 0.06 0.0302 0.0135 0.005 0.0018 6E-04 0.0001 3E-05
131 0.138 0.261 0.22 0.162 0.11 0.0626 0.0315 0.0144 0.006 0.002 6E-04 0.0002 6E-04
139 0.134 0.253 0.21 0.162 0.11 0.0645 0.0349 0.0166 0.007 0.0026 1E-04 0.0003 6E-04
151 0.128 0.244 0.21 0.159 0.11 0.0718 0.0395 0.0189 0.009 0.0035 0.001 0.0005 2E-04
199 0.112 0.217 0.19 0.157 0.12 0.0832 0.0537 0.0325 0.018 0.0091 0.004 0.0017 6E-04
  1. Family B is made from the cross-correlation or dot products of A. The strength of the correlation is optimally low in the second left column and increases with each column to the right. The entries in italics mark the level at each p where the cross value becomes that of a perfect periodic autocorrelation. The sum of the entries on each row is normalized to 1. Bold entries mark the array size p where each correlation level has maximum frequency