Three experimental pearls in Costas arrays
نویسنده
چکیده
The results of 3 experiments in Costas arrays are presented, for which theoretical explanation is still not available: the number of dots on the main diagonal of exponential Welch arrays, the parity populations of Golomb arrays generated in fields of characteristic 2, and the maximal cross-correlation between pairs of Welch or Golomb arrays generated in fields of size equal to a Sophie Germain prime.
منابع مشابه
Algebraic Symmetries of Generic Multidimensional Periodic Costas Arrays and their importance in the enumeration of Multidimensional Periodic Sonar Arrays
We present two symmetries of the generic multidimensional periodic Costas arrays over elementary abelian groups. Through exhaustive search, we observe that these two symmetries generate the Costas arrays for the enumeration up to p = 5 (5x5x24). Following the results, we conjecture that these generators characterize the group of symmetries of the generic (m+1)-dimensional periodic Costas arrays...
متن کاملAlgebraic Constructions for Costas Arrays
Thus, if ai,,j, = ail,il= ajl,j, = aiJqj4 = 1 in the matrix, we must not have ii2 1 il 3jjL;$) = (i4 4 ,.i, -jd, nor may we have (iz i,,j, -j,)= . ,. . 13 ‘2, 3 Such matri& have been called either Costas Arrays or constellations in Ref. [2], which explores constructions as well as applications for these patterns. It is convenient to represent these arrays on an n X n grid, using dots for the l’...
متن کاملCommon distance vectors between Costas arrays
We investigate the distance vectors contained in individual Costas arrays and in pairs of Costas arrays, and prove some rigorous results in the case of the algebraically constructed arrays. Overall, it appears that the set with the property that every Costas array has a distance vector in this set, or that every pair of Costas arrays with a common vector have a common vector in this set, is in ...
متن کاملThree challenges in Costas arrays
We present 3 open challenges in the field of Costas arrays. They are: a) the determination of the number of dots on the main diagonal of a Welch array, and especially the maximal such number for a Welch array of a given order; b) the conjecture that the fraction of Welch arrays without dots on the main diagonal behaves asymptotically as the fraction of permutations without fixed points and henc...
متن کاملThe enumeration of Costas arrays of order 28 and its consequences
The results of the enumeration of Costas arrays of order 28 are presented: all arrays found are accounted for by the Golomb and Welch construction methods, making 28 the first order (larger than 5) for which no sporadic Costas arrays exist. The enumeration was performed on several computer clusters and required the equivalent of 70 years of single CPU time. Furthermore, a classification of Cost...
متن کامل