On the Measurement of the (Non)linearity of Costas Permutations

Table 1

Linearity results for all Costas permutations of orders 3≤𝑛≤27: the columns correspond from left to right to 𝑛, the minimal and maximal linearities observed, and the mean and standard deviations of the linearity.

𝑛	min 𝕃	max 𝕃	mean 𝕃	std 𝕃
3	2.4972	2.4972	2.4972	0
4	2.9750	3.7069	3.5083	0.3046
5	3.4886	4.3459	3.8902	0.2741
6	3.7244	5.1008	4.3918	0.3834
7	4.1534	5.1786	4.6496	0.2988
8	4.4234	5.9241	5.0275	0.2964
9	4.7015	6.8218	5.5497	0.3621
10	4.9301	7.4756	5.8875	0.3519
11	5.1913	7.6610	6.2660	0.3775
12	5.4815	8.5341	6.5952	0.3965
13	5.9015	8.7261	6.9115	0.4053
14	6.2014	9.4388	7.2270	0.4082
15	6.2186	9.8519	7.5333	0.4320
16	6.5159	11.0186	7.8509	0.4521
17	6.9582	11.4045	8.1315	0.4465
18	7.1846	12.9660	8.4167	0.4811
19	7.5165	12.4471	8.7136	0.4935
20	7.7579	11.8479	8.9461	0.4815
21	7.9894	13.9195	9.2645	0.5443
22	8.1603	15.2323	9.8122	0.9286
23	8.6376	14.7480	9.9175	0.8786
24	8.7028	15.9756	10.2508	1.0853
25	9.7256	16.5861	11.1684	1.5209
26	9.4019	14.8275	11.5788	1.6035
27	10.2502	16.8729	12.1096	1.4790