Welch-Costas array: Difference between revisions

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+#REDIRECT [[Costas array#Welch]]
-A '''Welch-Costas array''', or just Welch array, is a [[Costas array|Costas array]] generated using the following method, first discovered by [[Lloyd R. Welch]].
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-We take a primitive element, α, of a prime, p. We raise α to successive powers, modulo p. This creates a Costas permutation of length p-1. More formally, the dots defined by (i, α^i-1+c mod p) form a Welch array.
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+{{Radr|Welch–Costas array}}
-Example:
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-is a primitive element of 5.
-^1 = 3
-^2 = 9 = 4 (mod 5)
-^3 = 27 = 2 (mod 5)
-^4 = 81 = 1 (mod 5)
-Therefore [3 4 2 1] is a Costas permutation. More specifically, this is an exponential Welch array. The transposition of the array is a logarithmic Welch array.
-The number of Welch-Costas arrays which exist for a given size depends on the [[Euler's_totient_function|totient funtion]].
-==References==
-*[[Solomon_Golomb|S. Golomb]] and H. Taylor, ''Constructions and Properties of Costas Arrays'', PROC. IEEE, <b>72</b>, 9, SEPTEMBER 1984
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