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2000 Fiscal Year Final Research Report Summary

Construction Classification of weighing matrices of low order and its applications

Research Project

Project/Area Number 11640125
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionEhime University

Principal Investigator

OHMORI Hiroyuki  Ehime University, Department of Mathematics, Professor, 教育学部, 教授 (20036370)

Co-Investigator(Kenkyū-buntansha) SHIRAKURA Teruhiro  Kobe University, Department of Mathematics, Professor, 発達科学部, 教授 (30033913)
OKAMOTO Toshiaki  Ehime University, Faculty of Education, Associated Professor, 教育学部, 助教授 (50036414)
HIRATA Koichi  Ehime University, Faculty of Education, Professor, 教育学部, 教授 (80173235)
HAMADA Noboru  Osaka Woman University, Faculty of Science, Professor, 理学部, 教授 (90033844)
Project Period (FY) 1999 – 2000
Keywordsweighing matrix / semi-biplane / art gallery theorem / Holding and unholding / Fermat-like diophantine equation / orthogonal array / graphical enumeration / ternary linear code
Research Abstract

(1) Ohmori completed the classification of weighing matrices W (n, 6) of the semi-biplane type. And furthermore, he completed the classification of weighing matrices W (14,9)(in Japanese).
(2) Hirata gave another proofs of art gallery theorems and also showed that there are 17 different polyhedrons constructed from a development of a cube.
(3) Okamoto gave criteria on certain diophantine equations concerning Fermatlike equation over algebraic number fields.
(4) Shirakura discussed the optimality of orthogonal arrays and constructed. Furthermore, he gave the expornential generating function for some graphs.
(5) Hamada showed the nonexistence of some quaternary linear codes and a ternary linear code.

  • Research Products

    (16 results)

All Other

All Publications (16 results)

  • [Publications] H.Eguch and K.Hirata: "Alternate proofs of art gallery theorems"Mem.Fac.Educ.Ehime Univ.Nat.Sci.. 19(2). 17-22 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Toshiaki Okawoto: "Fermat-like diophantine equations"Mem.Fac.Educ.Ehime Univ.Nat.Sci.. 21(1). 1-6 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Mishima,M.Jimbo,T.Shirakura: "On the optimality of orthogonal arrays in case of cornelated errons"Journal of Statistical Planning and Inference. 88. 319-3*8 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] N.Hamad and T.Helleseth: "Arcs, blocking sets, and minihypers."Computers and Mathematics with Applications. 39. 159-168 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Noboru Hamada: "The non existence of quaternary linear codes with parameters [243,5,181], [248,5,185] and [240,5,179]"Ars Combinatoria. 51. 33-47 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hiroyuki,Ohmori: "Multivariate analysis, design of experiments, and surery sampling"Subir Ghosh. 663 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Y.OHNISHI and OHMORI: "Classification of weighing matrices W (14,9)"(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.EGUCHI and K.HIRATA: "Alternate proofs of art gallery theorems"Mem.Fac.Educ.Ehime Univ., Nat.Sci.. 19 (2). 17-22 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Koichi HIRATA: "Holding and unholding"Ehime Suugakkaishi. 40. 14-18 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Toshiaki OKAMOTO: "Fermat-like diophantine equations"Mem.Fac.Educ.Ehime Univ., Nat.Sci.. 21 (1). 1-6 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y.JIN, S.TAZAWA and T.SHIRAKURA: "Enumeration of connected graphs with cut vertices"JSPI. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.MISHIMA, M.JIMBO, T.SHIRAKURA: "On the optimality of orthogonal arrays in case of correlated errors"Journal of Statistical Planning and Inference. 88. 319-338 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] N.HAMADA, T.HELLESETH, H.MARTINSEN AND φ.YTREHUS: "There is no ternary [28,6,16] code"IEEE Transactions on Information Theory. 46. 1550-1554 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] N.HAMADA and T.HELLESETH: "Arcs, blocking sets, and minihypers"Computers and Mathematics with Applications. 39. 159-168 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Noboru HAMADA: "The nonexistence of quaternary linear codes with parameters [243,5,185]. [248,5,185] and [240,5,179]"Ars Combinatoria. 51. 33-47 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hiroyuki OHMORI: "Structure of weighing matrices of small order and weight, In S.Ghosh (Ed.), Multivariate analysis design of experiments, and survey sampling"Marcel Dekker, New York. 625-648 (2000)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2002-03-26  

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