Codes and Designs: Proceedings of a Conference Honoring Professor Dijen K. Ray-Chaudhuri on the Occasion of His 65th Birthday, the Ohio State University, May 18-21

334 Pages·2002·1.942 MB·English

by  Dijen Ray-Chaudhuri, Akos Seress

Ohio State University Mathematical Research Institute Publications 10
Editors: Gregory R.Baker, Walter D.Neumann, Karl Rubin
Ohio State University
Mathematical Research Institute Publications
1 Topology ’90, B.Apanasov, W.D.Neumann, A.W.Reid,
L.Siebenmann (Eds.)
2 The Arithmetic of Function Fields, D.Goss, D.R.Hayes,
M.I.Rosen (Eds.)
3 Geometric Group Theory, R.Charney, M.Davis, M.Shapiro (Eds.)
4 Groups, Difference Sets, and the Monster, K.T.Arasu, J.F.Dillon,
K.Harada, S.Sehgal, R.Solomon (Eds.)
5 Convergence in Ergodic Theory and Probability, V.Bergelson,
P.March, J.Rosenblatt (Eds.)
6 Representation Theory of Finite Groups, R.Solomon (Ed.)
7 The Monster and Lie Algebras, J.Ferrar, K.Harada (Eds.)
8 Groups and Computation III, W.M.Kantor, A´.Seress (Eds.)
9 Complex Analysis and Geometry, J.D.McNeal (Ed.)
Codes and Designs
Proceedings of a conference honoring
Professor Dijen K.Ray-Chaudhuri
on the occasion of his 65th birthday
The Ohio State University
(cid:2)
May 18 21, 2000
Editors
K.T.Arasu
´
A.Seress
≥
Walter de Gruyter · Berlin · New York 2002
Editors
K.T.Arasu
DepartmentofMathematicsandStatistics,WrightStateUniversity,Dayton,OH45435,USA
A´kosSeress
DepartmentofMathematics,TheOhioStateUniversity,Columbus,OH43210-1174,USA
SeriesEditors
GregoryR.Baker
DepartmentofMathematics,TheOhioStateUniversity,Columbus,OH43210-1174,USA
KarlRubin
DepartmentofMathematics,StanfordUniversity,Stanford,CA94305-2125,USA
WalterD.Neumann
DepartmentofMathematics,ColumbiaUniversity,NewYork,NY10027,USA
MathematicsSubjectClassification2000:05(cid:2)06;94(cid:2)06
(cid:2)(cid:2)Printedonacid-freepaperwhichfallswithintheguidelinesoftheANSI
toensurepermanenceanddurability.
LibraryofCongressCataloging-in-PublicationData
Codesanddesigns:proceedingsofaconferencehonoringPro-
fessor Dijen K.Ray-Chaudhuri on the occasion of his 65th
birthday, The Ohio State University, May 18(cid:2)21, 2000 / edi-
tors,K.T.Arasu,A´.Seress.
p. cm. (cid:2) (Ohio State University Mathematical
ResearchInstitutepublications;vol.10)
ISBN3110173964(acid-free-paper)
I.Arasu,K.T.,1954(cid:2) II.Seress,A´kos,1958(cid:2) III.Ohio
State University Mathematical Research Institute publica-
tions;10.
2002023667
DieDeutscheBibliothek(cid:2)Cataloging-in-PublicationData
Codes and designs : proceedings of a Conference Honoring
ProfessorDijenK.Ray-ChaudhuriontheOccasionofHis65th
Birthday, the Ohio State University, May 18(cid:2)21, 2000 / ed.
K.T.Arasu;A´.Seress.(cid:2)Berlin;NewYork:deGruyter,2002
(Ohio State University Mathematical Research Institute
publications;10)
ISBN3-11-017396-4
(cid:2)Copyright2002byWalterdeGruyterGmbH&Co.KG,10785Berlin.
Allrightsreserved,includingthoseoftranslationintoforeignlanguages.Nopartofthisbookmay
bereproducedinanyformorbyanymeans,electronicormechanical,includingphotocopy,recording,
oranyinformationstorageandretrievalsystem,withoutpermissioninwritingfromthepublisher.
PrintedinGermany.
Coverdesign:ThomasBonnie,Hamburg.
Typesetusingtheauthors’T Xfiles:I.Zimmermann,Freiburg.
E
Printingandbinding:Hubert&Co.GmbH&Co.KG,Göttingen.
Preface
Following an initiative of the late Professor Hans Zassenhaus in 1965, the Depart-
mentsofMathematicsattheTheOhioStateUniversityandDenisonUniversityhave
been holding conferences in Combinatorics, Group Theory, and Ring Theory. Ini-
tially,thesemeetingshavebeenheldannually,andlaterbiannually;intheyear2000,
the 25th meeting of this series was conducted. These conferences have primarily
attracted mathematicians from institutions in Ohio and nearby states, but there have
beenmanyparticipantsfromotherpartsofthecountry,aswellasfromabroad. There
are usually twenty to thirty invited 20-minute talks given in each of the three main
areas. However, at the last conference, held during May 18–21, 2000 on the Ohio
State main campus in Columbus, there was a special addition to the Combinatorics
program in tribute to the 65th birthday of Dijen Ray-Chaudhuri. The Dijen 65 part
oftheconferenceconsistedoffourteen40-minutelecturesbyeitherformerstudents
ofDijenorothermathematicianswithstrongpersonalandprofessionaltieswithhim.
ThetopicsrangedfromCodingTheory,DesignTheory,GeometryandOptimization
toGraphTheory,reflectingthewiderangeofareastowhichProfessorRay-Chaudhuri
hasmadesubstantialcontributionsduringhisexemplarycareer.
Thebanquettocelebratehis65thbirthdayincludedremarksmadebyProfessors
R.M.Wilson,JeffKahn,ThomasDowling,andDr. JohnF.Dillon. Thehighlightof
thispartywasthepresentationoftheEulermedaltoProfessorRay-Chaudhuriforhis
life-longachievementsandcontributionstoCombinatorics. Thismedalwaspresented
to him by Professor Ralph Stanton on behalf of the Institute of Combinatorics and
Applications.
We are indebted to Professor Thomas Dowling for his invaluable help with the
organization of the combinatorics part of the conference, and to the referees of this
volume for their conscientious work. We are very grateful for the generous support
oftheMathematicalResearchInstituteofTheOhioStateUniversityandtheNational
SecurityAgency.
K.T.Arasu
ÁkosSeress

Table of contents
Preface.....................................................................v
ÁkosSeress
HighlightsofDijenRay-Chaudhuri’sresearch..............................1
K.T.Arasu,HenkD.L.Hollmann,KevinPlayer,andQingXiang
Onthep-ranksofGMWdifferencesets....................................9
SejeongBangandSung-YellSong
Characterizationofmaximalrationalcirculantassociationschemes..........37
MichelDeza
Face-regularpolyhedraandtilingswithtwocombinatorialtypesoffaces.....49
J.F.Dillon
Geometry,codesanddifferencesets:exceptionalconnections...............73
JeffreyH.DinitzandDouglasR.Stinson
AsingulardirectproductforbicolorableSteinertriplesystems..............87
DominicElviraandYutakaHiramine
Onsemi-regularrelativedifferencesetsinnon-abelianp-groups.............99
NickC.Fiala
Everyλ-designon6p+1pointsistype-1 ............................... 109
ChristianFremuth-PaegerandDieterJungnickel
Anintroductiontobalancednetworkflows...............................125
DerekW.HeinandYuryJ.Ionin
Ontheλ-designconjectureforv =5p+1points ........................ 145
viii Tableofcontents
HadiKharaghaniandVladimirD.Tonchev
Onaclassoftwinbalancedincompleteblockdesigns.....................157
Jon-LarkKimandVeraPless
Decodingsomedoubly-evenself-dual[32,16,8]codesbyhand............165
DonaldL.KreherandRolfS.Rees
Onthemaximumsizeofaholeinanincompletet-wisebalanced
designwithspecifiedminimumblocksize ............................... 179
WarwickdeLauney
OnafamilyofcocyclicHadamardmatrices..............................187
AkihiroMunemasa
AmassformulaforTypeIIcodesoverfinitefieldsofcharacteristictwo.....207
ErinJ.Schram
AposterioriprobabilitydecodingthroughthediscreteFouriertransform
andthedualcode......................................................215
MohanS.Shrikhande
Subdesignsofsymmetricdesigns ....................................... 237
IrfanSiap
LinearcodesoverF +uF andtheircompleteweightenumerators........259
2 2
N.J.A.Sloane
Onsingle-deletion-correctingcodes.....................................273
Zhe-XianWan
Criticalproblemsinfinitevectorspaces..................................293
RichardM.Wilson
ExistenceofSteinersystemsthatadmitautomorphismswithlargecycles....305
AndrewJ.Woldar
Rainbowgraphs.......................................................313
Dijen Ray-Chaudhuri