2016/03/22 by Kiermaier, Michael, Reinhard Laue, Laue, Reinhard +2
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Approximation and Integration #graph theory and CDMA systems
paper · doi:10.48550/arxiv.1603.06976
openalex publication_date 2016/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we show the existence of large sets LS2[3](2,k,v) for infinitely many values of k and v. The exact condition is v ≥ 8 and 0 ≤ k ≤ v such that for the remainders v and k of v and k modulo 6 we have 2 ≤ v < k ≤ 5. The proof is constructive and consists of two parts. First, we give a computer construction for an LS2[3](2,4,8), which is a partition of the set of all 4-dimensional subspaces of an 8-dimensional vector space over the binary field into three disjoint 2-(8, 4, 217)2 subspace designs. Together with the already known LS2[3](2,3,8), the application of a recursion method based on a decomposition of the Graßmannian into joins yields a construction for the claimed large sets.