The Non-Existence of Block-Transitive Subspace Designs

Autor: Daniel R. Hawtin, Jesse Lansdown

Let $q$ be a prime power and $V\cong{\mathbb F}_q^n$. A $t$-$(n,k,\lambda)_q$ design, or simply a subspace design, is a pair ${\mathcal D}=(V,{\mathcal B})$, where ${\mathcal B}$ is a subset of the set of all $k$-dimensional subspaces of $V$, with th

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7347cd10eebaa66daef46821f9f474f2
http://arxiv.org/abs/2102.05142

Alphabet-almost-simple 2-neighbour-transitive codes

Autor: Daniel R. Hawtin, Neil I. Gillespie

Publikováno v: Gillespie, N I & Hawtin, D R 2018, ' Alphabet-almost-simple 2-neighbour-transitive codes ', Ars Mathematica Contemporanea, vol. 14, no. 2, pp. 345-357 . < http://amc-journal.eu/index.php/amc/article/view/1240 >
Ars mathematica contemporanea

Let X be a subgroup of the full automorphism group of the Hamming graph H ( m , q ) , and C a subset of the vertices of the Hamming graph. We say that C is an ( X , 2) -neighbour-transitive code if X is transitive on C , as well as C 1 and C 2 , the

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f39738b6b4985bf26d7ba51321da4154
https://doi.org/10.26493/1855-3974.1240.515

$2$-Neighbour-Transitive Codes with Small Blocks of Imprimitivity

Autor: Neil I. Gillespie, Cheryl E. Praeger, Daniel R. Hawtin

Publikováno v: Gillespie, N I, Hawtin, D R & Praeger, C E 2020, ' 2-neighbour-transitive codes with small blocks of imprimitivity ', Electronic Journal of Combinatorics, vol. 27, no. 1, P1.42 . https://doi.org/10.37236/8040

A code C in the Hamming graph Γ = H(m, q) is a subset of the vertex set V Γ of the Hamming graph; the elements of C are called codewords. Any such code C induces a partition {C, C1, …, Cρ} of V Γ, where ρ is the covering radius of the code, ba

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::04685b39cfdb3d2b1d28231782dc91a3
http://arxiv.org/abs/1806.10514

$s$-Elusive Codes in Hamming Graphs

Autor: Daniel R. Hawtin

A code is a subset of the vertex set of a Hamming graph. The set of s-neighbours of a code is the set of all vertices at Hamming distance s from their nearest codeword. A code C is s-elusive if there exists a distinct code $$C'$$ that is equivalent t

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c93e5219651fd85ad56dcffee39622c1
http://arxiv.org/abs/1404.0950