2023/04/16 by Ingo Czerwinski, Alexander Pott · 1 voice
Computer Science · Engineering · Mathematics · #Cellular Automata and Applications #Coding theory and cryptography #Combinatorics #Dimension (graph theory) #Discrete mathematics #Mathematical analysis #Mathematics #Minimum distance #Order (exchange) #Set (abstract data type) #Sharpening #Upper and lower bounds #cs.IT #graph theory and CDMA systems #math.CO
paper · pdf · doi:10.3934/amc.2023054
arxiv published 2023/04/16 · openalex publication_date 2023/11/30 · arxiv updated 2024/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
Finding the maximum size of a Sidon set in \mathbbF2^t is of research interest for more than 40 years. In order to tackle this problem we recall a one-to-one correspondence between sum-free Sidon sets and linear codes with minimum distance greater or equal 5. Our main contribution about codes is a new non-existence result for linear codes with minimum distance 5 based on a sharpening of the Johnson bound. This gives, on the Sidon set side, an improvement of the general upper bound for the maximum size of a Sidon set. Additionally, we characterise maximal Sidon sets, that are those Sidon sets which can not be extended by adding elements without losing the Sidon property, up to dimension 6 and give all possible sizes for dimension 7 and 8 determined by computer calculations.