Some new large sets of geometric designs of type ${LS[3][2,3,2^8]}$

Journal of Algebra Combinatorics Discrete Structures and Applications

article

Michael R. Hurley¹  Bal K. Khadka¹  Spyros S. Magliveras¹ 

[1] Department of Mathematical Sciences, Florida Atlantic University

关键词: Geometric t-designs;    Large sets of geometric t-designs;    t-designs over GF(q);    Parallelisms;    Lattice basis reduction;    LLL algorithm;   

DOI  :  10.13069/jacodesmath.40139

学科分类：社会科学、人文和艺术（综合）

来源: Yildiz Technical University

【 摘 要 】

Let V be an n-dimensional vector space over Fq. By a geometric t-[qn, k, λ] design we mean acollection D of k-dimensional subspaces of V , called blocks, such that every t-dimensional subspace Tof V appears in exactly λ blocks in D. A large set, LS[N][t, k, qn], of geometric designs, is a collection ofN t-[qn, k, λ] designs which partitions the collection Vkof all k-dimensional subspaces of V . Prior torecent article [4] only large sets of geometric 1-designs were known to exist. However in [4] M. Braun,A. Kohnert, P. Östergard, and A. Wasserman constructed the world’s first large set of geometric2-designs, namely an LS[3][2,3,28], invariant under a Singer subgroup in GL8(2). In this work weconstruct an additional 9 distinct, large sets LS[3][2,3,28], with the help of lattice basis-reduction.

【 授权许可】

CC BY