2014/08/30 by Vivian Kuperberg, Kuperberg, Vivian · 1 citation
Computer Science · Engineering · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1409.0148
openalex publication_date 2014/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We use modular symmetric designs to study the existence of Hadamard matrices modulo certain primes. We solve the 7-modular and 11-modular versions of the Hadamard conjecture for all but a finite number of cases. In doing so, we state a conjecture for a sufficient condition for the existence of a p-modular Hadamard matrix for all but finitely many cases. When 2 is a primitive root of a prime p, we conditionally solve this conjecture and therefore the p-modular version of the Hadamard conjecture for all but finitely many cases when p ≡ 3 \pmod4, and prove a weaker result for p ≡ 1 \pmod4. Finally, we look at constraints on the existence of m-modular Hadamard matrices when the size of the matrix is small compared to m.