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STUDY OF CODING THEORY AND EXPERIMENTAL DESIGN

Research Project

Project/Area Number 09640286
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 InstitutionOSAKA PTRFECTURAL UNIVERSITY

Principal Investigator

HAMADA Noboru  OSAKA WOMEN'S UNIVERSITY,PROFESSOR, 学芸学部, 教授 (90033844)

Co-Investigator(Kenkyū-buntansha) KURIKI Shinji  OSAKA WOMEN'S UNIVERSITY,ASSISTANT PROFESSOR, 工学部, 助教授 (00167389)
AIZAWA Naruhiko  OSAKA WOMEN'S UNIVERSITY,ASSISTANT PROFESSOR, 学芸学部, 助教授 (70264786)
WATANABE Yutaka  OSAKA WOMEN'S UNIVERSITY,PROFESSOR, 学芸学部, 教授 (60028131)
WATANABE Takashi  OSAKA WOMEN'S UNIVERSITY,PROFESSOR, 学芸学部, 教授 (20089957)
ISHIHARA Kazuo  OSAKA WOMEN'S UNIVERSITY,PROFESSOR, 学芸学部, 教授 (90090563)
Project Period (FY) 1997 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥2,900,000 (Direct Cost: ¥2,900,000)
Fiscal Year 1998: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 1997: ¥1,700,000 (Direct Cost: ¥1,700,000)
Keywordscoding theory / experimental design / linear code / Griesmer bound / finite projective geometry / minihyper / ternary linear code / quaternary linear code
Research Abstract

Using Grant-in-Aid for Scientific Research of the Ministxy of Education under Contract Number 304-5009-09640286, we have the following results.
1. In the first paper [1] (cf. 11. References) by N.Hamada and M.van Eupen, it has been shown that there do not exist ternary [38, 6, 23] codes and ternary [39, 6, 24] codes and that n_3 (6, 23) = 39, d_3 (38, 6) = 22, n_3 (6, 24) = 40 and d_3 (39, 6) = 23.
2. In the second paper [2] by N.Hamada, it has been shown that there do not exist quaternaiy [293, 5, 219] codes, quaternary [289, 5, 216] codes and quaternary [277, 5, 207] codes and that n_4 (5, 219) = 294, n_4 (5, 216) = 290 and n_4 (5, 207) = 278.
3. In the third paper [3] by N.Harnada and Y.Watamori, it has been shown that there do not exist ternary [79, 6, 51] codes and that n_3 (6, 51) = 80.
4. In the fourth paper [4] by N.Hamada, it has been shown that there do not exist ternary [231, 6, 153] codes and ternary [204, 6, 135] codes and that n_3 (6, 153) 232 and n_3 (6, 135) = 205 or 206.
5. In the fifth paper [5] by N.Hamada, it has been shown that there do not exist quaternary [240, 5, 179] codes, quaternary [243, 5, 181] codes, quaternaiy [244, 5, 182] codes and quaternary [248, 5, 185] codes and that n_4 (5, 179) 241, n_4 (5, 181) = 244, n_4 (5, 182) 245 and n_4 (5, 185) = 249.

Report

(3 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report
  • Research Products

    (27 results)

All Other

All Publications (27 results)

  • [Publications] Noboru Hamada and Marijn van Eupen: "The nonexistence of ternary [38,6,23] codes" Designs,Codes and Cryptography. 13. 165-172 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Noboru Hamada: "On the nonexistence of some quaternary linear codes meeting the Griesmer bound" Journal of Statistical Planning and Inference. 72. 303-322 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Noboru Hamada and Yoko Watamori: "The nonexistence of ternary [79,6,51] codes" Journal of Statistical Planning and Inference. 72. 323-332 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Noboru Hamada: "The nonexistence of ternary [231,6,153] codes" Ars Combinatoria. 掲載決定. (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Noboru Hamada: "The nonexistence of quaternary linear codes with parameters [243,5,181],[248,5,185] and [240,5,179]" Ars Combinatoria. 掲載決定. (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Noboru Hamada and Marijn van Eupen: "The nonexistence of ternary [38,6,23] codes" Designs, Codes and Cryptography. Vol.13. 165-172 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Noboru Hamada: "On the nonexistence of some quaternary linear codes meeting the Griesmer bound" Journal of Statistical Planning and Inference. Vol.72. 303-322 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Noboru Hamada and Yoko Watamori: "The nonexistence of ternary [79,6,51] codes" Journal of Statistical Planning and Inference. Vol.72. 323-332 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Noboru Hamada: "The nonexistence of ternary [231,6,153] codes" Ars Combinatoria. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Noboru Hamada: "The nonexistence of quaternary linear codes with parameters [243,5,181], [248,5,185], and [240,5,179]" Ars Combinatoria. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Noboru Hamada and Marijn van Eupen: "The nonexistence of ternary[38,6,23]codes" Designs,Codes and Cryptography. 13. 165-172 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Noboru Hamada: "On the nonexistence of some quaternary linear codes meeting the Griesmer bound" Journal of Statistical Planning and Inference. 72. 303-322 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Noboru Hamada and Yoko Watamori: "The nonexistence of ternary[79,6,51]codes" Journal of Statistical Planning and Inference. 72. 323-332 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Noboru Hamada: "The nonexistence of ternary[231,6,153]codes" Ars Combinatoria. (掲載決定). (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] Noboru Hamada: "The nonexistence of quaternary linear codes with parameters[243,5,181],[248,5,185]and[240,5,179]" Ars Combinatoria. (掲載決定). (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] N.Hamada: "A necessary and sufficient condition for the existence of some ternary [n,k,d]codes meeting the Gniesmer bound" Designs,Codes and Cryptography. 10. 41-56 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] N.Hamada: "The nonexistence of ternary[29,6,17]codes" Mathematica Japonica. 46. 253-264 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] N.Hamada and T.Maekawa: "A characterization of some q-ary linear codes(q>(h-1)^2,h≧3)meeting the Griesmer bound:Part 2" Mathematica Japonica. 46. 241-252 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] N.Hamada and M.Uan Eupen: "The nonexistence of ternary[38,6,23]codes" Designs,Codes and Cryptography. 13. 165-172 (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] N.Hamada: "The nonexistence of ternary[231,6,153]codes" Ars Combinatoria. (掲載決定). (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] N.Hamada: "The nonexistence of quaternary linear codes with parameters[243,5,181],[248,5,185]and[240,5,179]" Ars Combinatoria. (印刷中). (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] N.Hamada: "On the nonexistence of some quaternary linear codes meeting the Griesmer bound" Journal of Statistical Planning and Inference. (掲載決定). (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] N.Hamada and Y.Watamori: "The nonexistence of ternary[79,6,51]codes" Journal of Statistical Planning and Inference. (掲載決定). (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] K.Ishihara and T.Yamamoto: "On nonlinear SOR-like methods,III-Global convergence of SOR and SSOR methods for convex problems" Japan Journal of Industrial and Applied Methematics. 15(掲載決定). (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] K.Ishihara and N.Aigawa: "Newton-secant method for complex nonlinear equations with nondifferentiable terms" Mathematica Japonica. 49(掲載決定). (1999)

    • Related Report
      1997 Annual Research Report
  • [Publications] T.Watanabe: "The KO-Cohomology ring of SU(2n)/SO(2n)" Glasgow Mathematical Journal. 39. 91-97 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] T.Watanabe: "Cohomology of a homogeneous space E_6/T^1・SU(6)" Proceedings of Symposia in Pure Mathematics. 63. 511-518 (1998)

    • Related Report
      1997 Annual Research Report

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Published: 1997-04-01   Modified: 2016-04-21  

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