EURASIP Journal on Advances in Signal Processing

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

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

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