Processing math: 100%

Proposed by Toby Walsh

These problems have many practical applications in communications and electrical engineering. The objective is to construct a binary sequence Si of length n that minimizes the autocorrelations between bits. Each bit in the sequence takes the value +1 or -1. With non-periodic (or open) boundary conditions, the k-th autocorrelation, Ck is defined to be nk1i=0SiSi+k. With periodic (or cyclic) boundary conditions, the k-th autocorrelation, Ck is defined to be n1i=0sisi+k mod n. The aim is to minimize the sum of the squares of these autocorrelations. That is, to minimize E=n1k=1C2k.