2026-10-13T00:37:41Z https://www.scidb.cn/oai

10.57760/sciencedb.43841 2026-07-28T17:19:19Z

2026-07-28 A Dataset of Optimal and Perfect Interval Sequences for Chinese Circular Rulers (Cyclic Golomb Rulers): An Independent Discovery up to 158 Intervals doi:10.57760/sciencedb.43841 en A Cyclic Golomb ruler (Chinese circular ruler) is a distance-measuring structure under modular arithmetic, where n marks are placed on a circle such that all clockwise distances between marks are distinct. A perfect ruler covers all integers from 1 to the ruler length L, while an optimal ruler covers the maximum possible set of consecutive integers. The author independently discovered and named this concept "Chinese circular ruler" over a decade ago while training students' thinking skills, and later learned that it had been previously studied internationally as "cyclic Golomb ruler." This dataset contains 199 optimal and perfect Chinese circular rulers computed by the author's self-developed program, with the largest number of intervals reaching 158, far exceeding the existing OEIS record of 18 intervals. Each entry provides the interval sequence, ruler length, and computation time. For certain orders (e.g., 7, 11, 13), perfect rulers are proven nonexistent, and only optimal rulers exist. All data have been verified against the internationally recognized OEIS sequences A004136 (shortest length) and A058241 (number of optimal rulers). This dataset can be directly used by researchers in combinatorics, coding theory, and communication systems, and serves as a benchmark for the design and verification of related algorithms. Chinese circular ruler; cyclic Golomb ruler; optimal ruler; perfect ruler; interval sequence; modular distance; independent discovery; OEIS A004136 ceng fei ge PUBLIC https://creativecommons.org/licenses/by/4.0/ dataset Science Data Bank