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A code $C$ in a generalised quadrangle ${\mathcal Q}$ is defined to be a subset of the vertex set of the point-line incidence graph $\varGamma$ of ${\mathcal Q}$. The minimum distance $\delta$ of $C$ is the smallest distance between a pair of distinc
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ab54194eb2f8b835f8117dc6d42ba27e
http://arxiv.org/abs/2105.05833
http://arxiv.org/abs/2105.05833
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
http://arxiv.org/abs/2102.05142
Autor:
Robert F. Bailey, Daniel R. Hawtin
A code $C$ in the Hamming metric, that is, is a subset of the vertex set $V\varGamma$ of the Hamming graph $\varGamma=H(m,q)$, gives rise to a natural distance partition $\{C,C_1,\ldots,C_\rho\}$, where $\rho$ is the covering radius of $C$. Such a co
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::611ddd5495d72aabccbb12778510d26d
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
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
Autor:
Cheryl E. Praeger, Daniel R. Hawtin
Publikováno v:
Journal of Combinatorial Theory, Series A. 171:105173
The main result here is a characterisation of binary $2$-neighbour-transitive codes with minimum distance at least $5$ via their minimal subcodes, which are found to be generated by certain designs. The motivation for studying this class of codes com
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
http://arxiv.org/abs/1806.10514
Autor:
Husam Osman, Emanuela Pelosi, Duncan A. Clark, Peter R. Hawtin, Hamid Jalal, Mary Ramsay, Mark Farrington, Adam Finn, John Magee, Andrew Turner, Anthony D. Hale, Ed Kaczmarski, Christina Atchison, David Carrington, Rohini Manuel, Sarah Collins, Shamez N Ladhani, Martin L’Estrange, David W. Brown
Publikováno v:
Journal of Infection. 71:128-131
Publikováno v:
Gillespie, N I, Hawtin, D R, Giudici, M & Praeger, C E 2016, ' Entry faithful 2-neighbour transitive codes ', Designs, Codes and Cryptography, vol. 79, no. 3, pp. 549-564 . https://doi.org/10.1007/s10623-015-0069-3
We consider a code to be a subset of the vertex set of a Hamming graph. The set of $s$-neighbours of a code is the set of vertices, not in the code, at distance $s$ from some codeword, but not distance less than $s$ from any codeword. A $2$-neighbour
Autor:
Rosemary A. Parslow, John Simms, Alex C. Conner, Zoe Lawson, Stuart R. Hawtin, Denise Wootten, Matthew T. Conner, Mark Wheatley
Publikováno v:
Journal of Biological Chemistry. 282:17405-17412
The roles of extracellular residues of G-protein-coupled receptors (GPCRs) are not well defined compared with residues in transmembrane helices. Nevertheless, it has been established that extracellular domains of both peptide-GPCRs and amine-GPCRs in