What are Golomb rulers and Sidon sets?
Golomb rulers are sets of positive integer numbers having all the differences between any pair of elements of the set to be unique. These numbers can be thought of as ruler marks (at integer locations) as an analogy with common rulers. Golomb rulers have many applications ranging from constructions for error correcting codes, to placement of radio telescopes in linear arrays. They were first studied by Babock in 1953 who was led to their definition to solve a problem in inteference between communication channels. Golomb was the first researcher to systematically study the subject in the 1960’s and since then his name is associated with these constructions. The function G(n), referred to as the length of an optimal Golomb ruler , is defined as the smallest possible length of a ruler with n marks. Sidon sets or B2 sequences is a related problem from combinatorial number theory. These sequences are subsets of 1,2,…,n having distinct pairwise sums between the elements. Sidon sets are nam
