2014/01/22 by Yanqing Wang, Xiaoming Li, Wang, Yanqing +1
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #Optimization and Control (math.OC) #graph theory and CDMA systems #math.NT #math.OC
paper · pdf · doi:10.48550/arxiv.1401.5556
8 pages
openalex publication_date 2014/01/22 · arxiv created 2014/01/27 · arxiv updated 2014/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Since the significance of Golomb Ruler Problem in some context, we proposes a function construction approach based on difference triangle to generate near-optimal Golomb rulers. Let x1, x2, ..., xn be an increasing sequence of integers, where x1 = 0, which satisfies the following conditions: if abs(xi-xj) = abs(xp-xq) then i, j = p,q. Our objective is to find the order of minimum xn for any given n. In this paper, the two results in a paper are both improved. In addition, it will be shown that the length of Golomb Ruler have been shortened to a half, and that the satisfying sequence can not be generated by such a quadratic formula as xi = ai2+bni+ci+dn2+en+f for any rational a, b, c, d, e and f.