2024/11/19 by Ingo Czerwinski, Alexander Pott, Czerwinski, Ingo +1
Mathematics · #11B13 #94D10 (Primary) 94B05 (Secondary) #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.2411.12911
openalex publication_date 2024/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A Sidon set M is a subset of \mathbbF2t such that the sum of four distinct elements of M is never 0. The goal is to find Sidon sets of large size. In this note we show that the graphs of almost perfect nonlinear (APN) functions with high linearity can be used to construct large Sidon sets. Thanks to recently constructed APN functions \mathbbF28→ \mathbbF28 with high linearity, we can construct Sidon sets of size 192 in \mathbbF215, where the largest sets so far had size 152. Using the inverse and the Dobbertin function also gives larger Sidon sets as previously known. Each of the new large Sidon sets M in \mathbbF2t yields a binary linear code with t check bits, minimum distance 5, and a length not known so far. Moreover, we improve the upper bound for the linearity of arbitrary APN functions.