Journal of Applied Mathematics / 2010 / Article / Tab 2 / Research Article
On the Measurement of the (Non)linearity of Costas Permutations Table 2 Linearity results for
- (a) and
- (b) permutations generated in
,
: the columns correspond from left to right to
, the minimal and maximal linearity observed, and the mean and standard deviations of the linearities.
(a)
min
max
mean
std
7 3.8344 3.8344 3.8344 0 11 4.7015 6.5598 5.9362 0.6950 13 5.1913 7.5414 6.4948 0.8282 17 6.2187 9.3125 7.8076 0.7503 19 7.6955 11.4045 8.9887 0.8291 23 8.2347 13.9195 9.9797 1.1294 29 10.2502 16.8729 12.0515 1.4318 31 10.9677 16.0584 13.0976 1.4772 37 11.2892 20.5871 14.8351 2.1180 41 12.7289 21.6292 16.1072 2.2266 43 12.6109 26.9280 17.1595 2.7143 47 13.6820 28.3311 18.3678 2.5944 53 14.7483 29.0807 20.7323 3.4550 59 16.5240 33.8105 23.1238 3.7493 61 18.0203 35.1987 23.8661 3.5871 67 17.9924 38.6901 26.2275 4.0515 71 19.2378 36.4151 27.6938 3.9807 73 18.1823 43.1096 28.6351 4.7167 79 19.4471 41.3463 30.9327 4.2014 83 21.2388 45.4478 32.5626 4.2763 89 21.3421 50.3580 35.0311 4.6115 97 24.6606 53.2888 38.2512 4.6876 101 27.1879 52.6007 39.8379 5.0796 103 25.4178 55.2598 40.6539 5.5482 107 27.3222 57.9382 42.2601 5.4518 109 24.9826 59.9810 43.1139 5.5113 113 29.6132 60.6273 44.7029 5.6808 127 32.5151 70.1353 50.4963 5.3487 131 31.2879 70.7198 51.9830 5.7581 137 37.2955 71.0958 54.4337 5.7566 139 39.2845 71.4561 55.2887 6.3653 149 40.5434 76.0981 59.2918 6.0764 151 37.4170 81.0333 60.1070 6.0674
(b)
min
max
mean
std
7 3.7880 4.8439 4.4465 0.4119 11 5.5053 7.4756 6.1462 0.4734 13 6.5154 8.5341 7.3052 0.6860 17 7.0501 11.0186 8.5779 0.8158 19 7.5172 12.9660 9.2807 1.1130 23 8.9254 15.2323 10.6936 1.2187 29 10.3331 18.3192 12.9565 1.8357 31 10.9192 19.9770 13.5635 1.6404 37 11.9643 24.3642 15.7800 2.5823 41 12.7863 25.1720 17.1771 2.8822 43 12.7419 25.3322 17.8591 3.0673 47 14.0212 28.1627 19.1228 3.2689 53 15.0066 33.3970 21.5939 3.8445 59 16.4316 35.5213 23.5966 4.3340 61 16.2902 36.1331 24.3684 4.5547 67 17.4479 39.8553 26.7267 4.9172 71 18.4225 40.7985 28.2850 5.0988 73 18.3244 42.1267 29.0482 5.1430 79 18.5635 47.8331 31.4486 5.5526 83 20.0101 49.1780 33.0352 5.6957 89 21.2534 51.4717 35.4218 5.5741 97 22.1986 57.7464 38.6617 6.2288 101 22.9944 56.8656 40.2868 6.6020 103 25.5362 57.2796 41.0855 6.5606 107 24.0941 63.6045 42.7078 6.5930 109 24.7888 64.2623 43.5123 6.6427 113 26.5017 64.3054 45.1397 7.0107 127 35.1980 65.9180 50.7644 6.1753 131 30.9777 73.9441 52.4322 7.4101 137 32.7740 77.6968 54.8584 7.5626 139 31.6170 79.5067 55.6664 7.5732 149 35.0306 83.2909 59.7193 7.8052 151 36.3423 84.3540 60.5394 8.0897