A Golomb-Costas array is an arrangement of dots and blanks,rndefined for each positive integer power of a prime and satisfying certain unusualrnconditions. A dot occurring in such an array is an even/even position if itrnoccurs in the I-th row and j-th column,where I and j are both even integers,rnand there are similar definitions of odd/odd,even/odd and odd/even positionsrnfor dots. When q is a power of an odd prime,we enumerate the number ofrneven/even,odd/odd,even/odd and odd/even positions for dots in a Golomb-rnCostas array of order q ? 2. We show that three of these numbers are equalrnand they differ by ±1 from the fourth. More general Costas arrays do notrnexhibit this regularity. We also show that if q = rt,where r is a power of arnprime and t is an integer greater than 1,any Golomb-Costas array of orderrnq ? 2 contains in a natural way a Golomb-Costas array of order r ? 2 whichrncan easily be identified.
展开▼
