Zobrazeno 1 - 10
of 20
pro vyhledávání: '"Gary R. W. Greaves"'
Autor:
Gary R. W. Greaves, Jeven Syatriadi
Publikováno v:
IEEE Transactions on Information Theory. 65:4764-4770
We give constructions of some special cases of [n, k] Reed-Solomon codes over finite fields of size at least n and n + 1 whose generator matrices have constrained support. Furthermore, we consider a generalization of the GM-MDS conjecture proposed by
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5b8cb079f0b17ec0477b1db07c9ba52e
https://doi.org/10.1109/tit.2019.2897767
https://doi.org/10.1109/tit.2019.2897767
Autor:
Gary R. W. Greaves, Pavlo Yatsyna
Publikováno v:
Mathematics of Computation. 88:3041-3061
For $e$ a positive integer, we find restrictions modulo $2^e$ on the coefficients of the characteristic polynomial $\chi_S(x)$ of a Seidel matrix $S$. We show that, for a Seidel matrix of order $n$ even (resp. odd), there are at most $2^{\binom{e-2}{
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::00a9d8159c7a421dc5dbd27ee08e8edb
https://doi.org/10.1090/mcom/3433
https://doi.org/10.1090/mcom/3433
Publikováno v:
Linear Algebra and its Applications. 564:201-208
It is proved that for any finite connected graph G, there exists an orientation of G such that the spectral radius of the corresponding Hermitian adjacency matrix is smaller or equal to the spectral radius of the universal cover of G (with equality i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5f9a2f90088ccf3861fd8ff71254aa12
https://doi.org/10.1016/j.laa.2018.12.004
https://doi.org/10.1016/j.laa.2018.12.004
We show that the maximum cardinality of an equiangular line system in 14 and 16 dimensions is 28 and 40, respectively, thereby solving a longstanding open problem. We also improve the upper bounds on the cardinality of equiangular line systems in 19
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::aaa794f270cbc50e71665e9a93956888
https://hdl.handle.net/10356/152761
https://hdl.handle.net/10356/152761
We introduce the study of frames and equiangular lines in classical geometries over finite fields. After developing the basic theory, we give several examples and demonstrate finite field analogs of equiangular tight frames (ETFs) produced by modular
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bfa224dc89a2965f1b80e42b96dd9eea
http://arxiv.org/abs/2012.12977
http://arxiv.org/abs/2012.12977
Autor:
Gary R. W. Greaves, Sho Suda
Publikováno v:
Journal of Combinatorial Designs. 27:123-141
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b15777de4fcf0124819e5996068b8fcd
https://doi.org/10.1002/jcd.21626
https://doi.org/10.1002/jcd.21626
Publikováno v:
European Journal of Combinatorics. 97:103384
In this paper, we study the order of a maximal clique in an amply regular graph with a fixed smallest eigenvalue by considering a vertex that is adjacent to some (but not all) vertices of the maximal clique. As a consequence, we show that if a strong
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d44193b3808fcc8a7fe6bc21d563ef40
https://doi.org/10.1016/j.ejc.2021.103384
https://doi.org/10.1016/j.ejc.2021.103384
Autor:
Sho Suda, Gary R. W. Greaves
Publikováno v:
Journal of Combinatorial Designs. 25:507-522
We show that the existence of {±1}-matrices having largest possible determinant is equivalent to the existence of certain tournament matrices. In particular, we prove a recent conjecture of Armario. We also show that large submatrices of conference
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a3646166c0148e00019bfc79637d0fca
https://doi.org/10.1002/jcd.21567
https://doi.org/10.1002/jcd.21567
Autor:
Gary R. W. Greaves, Jack H. Koolen
We exhibit a new construction of edge-regular graphs with regular cliques that are not strongly regular. The infinite family of graphs resulting from this construction includes an edge-regular graph with parameters (24,8,2). We also show that edge-re
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9e54c31ea65be4b8c0864cd9e3172028
https://hdl.handle.net/10356/137229
https://hdl.handle.net/10356/137229
Publikováno v:
Journal of Combinatorial Theory, Series B. 110:90-111
We give a structural classification of edge-signed graphs with smallest eigenvalue greater than -2. We prove a conjecture of Hoffman about the smallest eigenvalue of the line graph of a tree that was stated in the 1970s. Furthermore, we prove a more
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::462b4276108a2be51e0fa0d453257d03
https://doi.org/10.1016/j.jctb.2014.07.006
https://doi.org/10.1016/j.jctb.2014.07.006