Skip to main content

Advertisement

Table 2 Distribution of cross-correlation values between family A and p p × p equivalent Hadamard variant

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

p = 4k-1 Frequency of increasing cross-correlation level
  1 2 3 4 5 6 7 8 9 10
7 0.5182 0.4519 0.0299 0 0 0     
11 0.4324 0.4879 0.0774 0.0023 0 0 0    
19 0.3443 0.4769 0.1556 0.0222 0.001 0 0 0   
23 0.3158 0.4639 0.1812 0.0358 0.0032 0.0001 6E-06 0 0  
31 0.2755 0.4354 0.2135 0.0635 0.011 0.001 5E-05 9E-07 0  
43 0.2356 0.396 0.2381 0.0979 0.0275 0.005 0.0006 0.0001 0 0
47 0.2283 0.3857 0.2373 0.1064 0.0335 0.0075 0.0013 0.0001   
59 0.2041 0.3571 0.2416 0.1271 0.0508 0.0154 0.0033 0.0005 0 0
67 0.1913 0.3419 0.2417 0.1361 0.0606 0.0211 0.0058 0.0012 0.0002 4E-05
71 0.1862 0.3342 0.2416 0.1397 0.0648 0.0243 0.0071 0.0017 0.0003 0
79 0.1766 0.3206 0.2393 0.1464 0.0736 0.0301 0.01 0.0027 0.0006 0.0001
83 0.1721 0.3148 0.2386 0.1486 0.0764 0.0337 0.0115 0.0034 0.0079 0.0014
103 0.1546 0.2888 0.2302 0.1567 0.0924 0.0467 0.0201 0.0072 0.0024 0.0006
127 0.1404 0.2637 0.2189 0.1614 0.1042 0.06 0.0302 0.0135 0.0052 0.0018
131 0.1375 0.2606 0.2166 0.1622 0.1059 0.0626 0.0315 0.0144 0.0058 0.002
139 0.1342 0.2531 0.2147 0.1618 0.109 0.0645 0.0349 0.0166 0.0072 0.0026
151 0.1278 0.2438 0.2109 0.1586 0.114 0.0718 0.0395 0.0189 0.0094 0.0035
199 0.1118 0.2168 0.1927 0.1565 0.119 0.0832 0.0537 0.0325 0.0178 0.0091
  1. 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-correlation becomes an autocorrelation. The sum of the entries on each row is normalized to 1. Bold entries mark the array size p where the maximum frequency for level i occurs