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Two new optimal ternary two-weight codes and strongly regular graphs

1996
*
Discrete Mathematics
*

Based upon the code

doi:10.1016/0012-365x(94)00264-j
fatcat:zjmgx6i54vee3alfscsto7kcza
*parameters*, the existence of two*strongly**regular**graphs*is established. ... It is well known that two-weight codes result in*strongly**regular**graphs*if the code is projective. ... Andries Brouwer for bringing this connection between codes and*graphs*to his attention. ...##
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A new two-weight code and strongly regular graph

1996
*
Applied Mathematics Letters
*

It is well known that two-weight codes result in

doi:10.1016/0893-9659(96)00004-3
fatcat:ufmzjsdsdzhazcpcffpaan5esq
*strongly**regular**graphs*if the code is projective. In this paper*a*(154,6,99)*quasi*-cyclic two-weight code over OF (3) is presented. ... Let C be*a*linear (*n*,*k*, d) code over GF(q). ... Many QC codes were found*with*dmin --99, but*one*was found*with*only*one*other nonzero weight. This search took less than*1*minute*on**a*SUN SPARCstation 2 computer. ...##
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Page 798 of Mathematical Reviews Vol. , Issue 90B
[page]

1990
*
Mathematical Reviews
*

The authors give
both constructions and nonexistence results and provide

*a*table listing all feasible*parameter*sets for primitive*strongly**regular**graphs**with**a**strongly**regular*decomposition and < 300 ... G. (*1*-MI)*Strongly**regular**graphs**with**strongly**regular*decomposition. Linear Algebra Appl. 114(115) (1989), 379-398. ...##
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HOW TO SELECT PAIRED COMPARISONS IN AHP OF INCOMPLETE INFORMATION-STRONGLY REGULAR GRAPH DESIGN

1998
*
Journal of the Operations Research Society of Japan
*

Since SR

doi:10.15807/jorsj.41.311
fatcat:f5wnegalifchra4nrvei3abndq
*graphs*are rather diMcult to be constructed, we generalize them to*quasi*-*strongly**regular*(*quasi*-SR)*graphs*, and propose*quasi*-SR design based*on**quasi*-SR*graphs*. ... The problem is how to select pairs to be compared in S., that is,*a*design to get data, We propose the*strongly**regular*(SR) design based*on**strongly**regular**graphs*, and by numerical simulatiDn show that ... More precisely, for given*n*, what is the best subset of size m to be selected in S., to estimate We propose the*strongly**regular*(SR) design based*on**strongly**regular**graphs*, and by numerical simulation ...##
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Quasi-residual designs, 112-designs, and strongly regular multigraphs

1995
*
Discrete Mathematics
*

Suppose that the

doi:10.1016/0012-365x(94)00014-a
fatcat:ai7b6skkw5hl3jnx7vvhj53sqm
*parameters*(m,*n*, u, y, R) of*a**strongly**regular*multigraph can be written in the form m =*k*,*n*=r-i, u=k2A, y=*k*(*k*-l)(*A*-l), R=*k*(r-*1*) for some integers*k*2 3, r and*1*. ... Suppose that r is*a**strongly**regular*multigraph whose*parameters*(m,*n*, u, y, R) can be written in the form m = r,*n*=*k*+ r + c -1t, p = rt, y = rc, R = r(kl),*with*integers r 2 3 and t 2*1*, and real ... The collinearity*graph*of*a*l~design*with**parameters*(r,*k*, t, c) is*a**strongly**regular*multigraph*with**parameters*(m,*n*, p, y, R) given by (1.6) m:= r,*n*:=*k*+r+c-l-t, u=rt, y:=rc, R:=r(*k*-*1*). ...##
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Steiner triple systems and strongly regular graphs

1969
*
Journal of Combinatorial Theory
*

The Steiner triple systems are characterized in terms of

doi:10.1016/s0021-9800(69)80102-x
fatcat:ckkdqjyko5br3l772pkb57vg2i
*strongly**regular**graphs*provided that the number of cliques exceed 67. ...*A*.*A*. Zykov for inviting the second author to Novosibirsk and thus providing the facilities for our joint work, which we do hope to continue. ... Bose and Laskar [3] considered*graphs*G*with*the following properties: (C1) G is connected and*regular*of valence r(*k*--*1*). (*C2*) G is edge*regular**with*edge degree (*k*--2) q-*a*. ...##
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Hereditarily extended properties, quasi-random graphs and not necessarily induced subgraphs

1997
*
Combinatorica
*

Here the properties are

doi:10.1007/bf01195005
fatcat:riblmkxljrf4bn2tcj7ml7qoqe
*strongly*connected to counting not necessarily induced subgraphs of*a*given type, while in*a*subsequent paper we shall investigate the properties connected*with*counting induced ... Dedicated to the memory of Paul Erdbs Recently nmch attention has been focused*on*the theory of*quasi*-random*graph*and hypergraph properties. ... U V (*n*) be*a*Szemer6di Partition of Gn*with*the*parameters*gt = ~, ~ = t. Let X C Vi, IX[ = 89 Suppose all the pairs (vi(*n*),vj(*n*)),--l<i<j<,-*1*are g-*regular*. ...##
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Trivial pursuit: Remarks on the main gap

1987
*
Annals of Pure and Applied Logic
*

*A*dependence relation is trivial when

*a*single point which depends

*on*

*a*pair of independent points depends

*on*just

*one*of them. ... Section

*1*of this paper contains some technical results about trivial types. ... Let p, q E S(

*A*) be stationary trivial types

*with*p ,

*k*! q. Suppose p is

*regular*and for some +, (q, C#J) is

*strongly*

*regular*. ...

##
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Quasi-quadrics and related structures

2000
*
The Australasian Journal of Combinatorics
*

When

dblp:journals/ajc/ClerckHOP00
fatcat:rmguzexhbfej7lyas4rx3vf4wq
*n*is even,*quasi*-quadrics have three sizes of intersection*with*respect to hyperplanes. Certain of these may be used to construct antipodal distance*regular*covers of complete*graphs*. ... In*a*projective space PG(*n*, q)*a**quasi*-quadric is*a*set of points that has the same intersection numbers*with*respect to hyperplanes as*a*nondegenerate quadric in that space. ... ,bd-*1*;C1,*C2*,'" ,Cd}' The*graph*r is*strongly**regular**with**parameters*(IV\,*k*, ,\, /-l) if it is*regular**with*valency*k*and if the number of vertices joined to two given adjacent vertices is*A*and the number ...##
###
Cheeger isoperimetric constant of Gromov hyperbolic manifolds and graphs
[article]

2016
*
arXiv
*
pre-print

We characterize the hyperbolic manifolds and

arXiv:1605.04394v1
fatcat:6u62fn44ijgghkvaswvq3k73li
*graphs*(*with*bounded local geometry) verifying this isoperimetric inequality, in terms of their Gromov boundary. ... Furthermore, we characterize the trees*with*isoperimetric inequality (without any hypothesis). ... Let {G*k*}*k*∈*N*be*a*sequence of*graphs*isometric to G*with*v*k*∈ V (G*k*) for each*k*∈*N*. ...##
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Nonlinear Quantum Search
[article]

2015
*
arXiv
*
pre-print

Jointly optimizing these resources results in an overall scaling of

arXiv:1506.04388v1
fatcat:bnpwjxqidja6ziovukeaokttse
*N*^*1*/4, which is*a*significant, but not unreasonable, improvement over the*N*^*1*/2 scaling of Grover's algo. ... Further,*strongly*reg*graphs*, which have no global sym, are sufficiently complete for quant search*on*them to asymp behave like unstruct search. ...*graph*, which is*a**strongly**regular**graph**with**parameters*(10,3,0,1). ...##
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Effect of fluctuations on the NMR relaxation beyond the Abrikosov vortex state

2015
*
Physical Review B
*

The first

doi:10.1103/physrevb.92.054513
fatcat:x255m4ny6fccxmsqh4hlqtfuma
*one*is its decrease in result of suppression of*quasi*-particle density of states (DOS) due to formation of fluctuation Cooper pairs (FCP). ... As*a*result, different scenarios*with*either growth or decrease of the NMR relaxation rate are possible upon approaching the normal metal - type-II superconductor transition. ... ACKNOWLEDGEMENTS We express our deep gratitude to*A*. Rigamonti and*A*. Lasciafari for attracting our attention to their experiments and numerous elucidating discussions. ...##
###
Page 1310 of Mathematical Reviews Vol. , Issue 91C
[page]

1991
*
Mathematical Reviews
*

The friendship theorem says that the

*graph*cannot be*regular*for*A*=*1*. The authors would like to generalize this to the nonexistence of*strongly**regular**graphs**with*constant*A*= and x. ... Stembridge (*1*-MI) 91c:05202 05E30 Hartnell, Bert L. (3-STMR); Jeans, Neville (3-MB); Kocay, William (3-MB)*Parameter*sets for*a*class of*strongly**regular**graphs*. J. Combin. Math. Combin. ...##
###
Rigidity for Quasi-Möbius Actions on Fractal Metric Spaces
[article]

2016
*
arXiv
*
pre-print

Kleiner proved

arXiv:1308.0639v2
fatcat:gtcsf422krabbazwvc5sfzsaii
*a*rigidity theorem for expanding*quasi*-Möbius group actions*on*Ahlfors*n*-*regular*metric spaces*with*topological dimension*n*. ... This led naturally to*a*rigidity result for*quasi*-convex geometric actions*on*CAT(-*1*)-spaces that can be seen as*a*metric analog to the "entropy rigidity" theorems of U. Hamenstädt and M. Bourdon. ... Let Z be*a*compact, Ahlfors*n*-*regular*met- ric space*with*topological dimension*n*≥*1*. Suppose that Γ y Z is*a*uniformly*quasi*-Möbius group action that is cocompact*on*triples. ...##
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Regularized and inertial algorithms for common fixed points of nonlinear operators

2008
*
Journal of Mathematical Analysis and Applications
*

This paper deals

doi:10.1016/j.jmaa.2008.03.028
fatcat:gt5trm2wx5bmrjc7yxnswsefue
*with**a*general fixed point iteration for computing*a*point in some nonempty closed and convex solution set included in the common fixed point set of*a*sequence of mappings*on**a*real Hilbert ... Under classical conditions*on*the operators and the*parameters*, we prove that the sequence of iterates generated by our scheme converges*strongly*to the element of minimal norm in the solution set. ... However the products T*n*of*a**quasi*-nonexpansive mapping T are obviously*quasi*-nonexpansive, hence not necessarily continuous (for*n*large enough),*on*the contrary to the case when T is asymptotically ...
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