2012/03/04 by Alexander A. Davydov, Davydov, Alexander A., Giorgio Faina +7 · 1 citation
Computer Science · Engineering · Mathematics · #05B25 #05C10 #94B05 #Advanced Wireless Communication Techniques #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems #math.CO #msc:05B25 #msc:05C10 #msc:94B05
paper · pdf · doi:10.48550/arxiv.1203.0709
39 pages, 8 tables
arxiv created 2012/03/04 · openalex publication_date 2012/03/04 · arxiv updated 2012/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The spectrum of possible parameters of symmetric configurations is investigated. We both survey known constructions and results, and propose some new construction methods. Many new parameters are obtained, in particular for cyclic symmetric configurations, which are equivalent to deficient cyclic difference sets. Both Golomb rulers and modular Golomb rulers are a key tool in our investigation. Several new upper bounds on the minimum integer E(k) such that for each v >= E(k) there exists a symmetric configuration vk are obtained. Upper bounds of the same type are provided for cyclic symmetric configurations. From the standpoint of applications, it should be noted that our results extend the range of possible parameters of LDPC codes, generalized LDPC codes, and quasi-cyclic LDPC codes.