1995 Fiscal Year Annual Research Report

符号理論と組合せ論の研究

Research Project

Project/Area Number	07640326
Research Institution	Osaka Women's University
Principal Investigator	濱田昇大阪女子大学, 学芸学部, 教授 (90033844)
Co-Investigator(Kenkyū-buntansha)	大内本夫大阪女子大学, 学芸学部, 助教授 (70127885) 渡辺豊大阪女子大学, 学芸学部, 教授 (60028131) 渡辺孝大阪女子大学, 学芸学部, 教授 (20089957) 堤陽大阪女子大学, 学芸学部, 教授 (30029631) 石原和夫大阪女子大学, 学芸学部, 教授 (90090563)
Keywords	符号理論 / 組合せ論 / 線形符号 / Griesmer bound / 有限射影幾何 / minihyper / ternary linear code / quaternary linear code
Research Abstract	符号長がn、次元がk、最小距離がdであるq元線形符号を[n,k,d;q]-codeという。与えられた整数k,d,qに対してGriesmer boundの等号を満たす[n,k,d;q]-codeが存在するならば、この符号は最適な符号であることが知られている。この研究の目的は次の2つの問題を解くことである。 (問題A)Griesmer boundの符号を満たす[n,k,d;q]-codeが存在するためのk,d,qに対する必要十分条件を求めよ。 (問題B)与えられた整数k,d,qに対して、Griesmer boundの等号を満たす[n,k,d;q]-codeが存在する場合には、Griesmer boundの等号を満たす同値でないすべての[n,k,d;q]-codeを構成し、特徴付けをせよ。この研究の代表者である濱田昇は1987年に、1≦d≦q^<k-1>の場合には、問題Aを解くためには、有限射影幾何PG(k-1,q)の中に{V_k-n,V_<k-1>-n+d;k-1,q}-minihyperが存在するためのk,d,qに対する必要十分条件を求めればよいこと、および、問題Bを解くためには{V_k-n,V_<k-1>-n+d;k-1,q}-minihyperの特徴付けをすればよいことを示した。今回はq=3 or 4,k≧3,1≦d<q^<k-1>の場合に対して{V_k-n,V_<k-1>-n+d;k-1,q}-minihyperが存在するかどうかを調べ、存在する場合にはそのminihyperの特徴付けをした。これらの研究実績は研究発表(雑誌論文)の欄の1から12までの12個の論文として学術雑誌に掲載(または掲載決定)された。

Research Products
(17 results)

All Other

All Publications (17 results)

[Publications] N.Hamada: "construction of some optimal ternary linear codes and the uniqueness of〔294,6,195;3〕-codes meeting the Griesmer bound" Finite Fields and Their Application. 1. 458-468 (1995)
[Publications] N.Hamada: "A characterization of some{3U_<μ+1>,3U_μ;k-1,q}-minihyper and some〔n,k,q^<k-1>-3q^μ;q〕-codes meeting the Griesmer bound" Discrete Mathematics. 146. 59-67 (1995)
[Publications] N.Hamada: "A characterization of some{31,9;4,3}-minihypers and some〔90,5,59;3〕-codes meeting the Griesmer bound" Mathematica Japonica. 41. 657-672 (1995)
[Publications] M.van Eupen,N.Hamada: "The nonexistence of ternary〔50,5,32〕codes" Designs,Codes and Cryptography. 7. 235-237 (1995)
[Publications] N.Hamada: "The nonexistence of some quaternary linear codes meeting the Griesmer bound and the bounds for n_4(5,d),1≦d≦256" Mathematica Japonica. 43. 7-21 (1996)
[Publications] N.Hamada: "A characterization of{43,13;4,3}-minihypers and projective ternary〔78,5,51;3〕-codes" Mathematica Japonica. 43. 253-266 (1996)
[Publications] N.Hamada: "A necessary and sufficient condition for the existence of some ternary〔n,k,d〕codes meeting the Griesmer bound" Designs,Codes and Cryptography. 8(印刷中). (1996)
[Publications] N.Hamada: "The nonexistence of〔71,5,46;3〕-codes" Journal of Statistical Planning and Inference. 50(印刷中). (1996)
[Publications] N.Hamada: "The nonexistence of some ternary linear codes of dimension 6 and the bounds for n_3(6,d),1≦d≦243" Mathematica Japonica. 43(印刷中). (1996)
[Publications] N.Hamada: "A characterization of some{25,7;3,3}-minihypers and some〔15,4,9;3〕-codes with B_2=0" Journal of Statistical Planning and Inference. 51(印刷中). (1996)
[Publications] N.Hamada: "The uniqueness of〔87,5,57;3〕-codes and the nonexistence of〔258,6,171;3〕-codes" Journal of Statistical Planning and Inference. 51(印刷中). (1996)
[Publications] N.Hamada: "The nonexistence of ternary〔231,6,153〕codes" Ars Combinatoria. (掲載決定). (1996)
[Publications] K.Ishihara: "On the optimum SOR iterations for finite difference approximation to periodic boundary value problems" Mathematica Japonica. 41. 199-209 (1995)
[Publications] K.Ishihara: "Optimum SOR iterations for finite difference equations arising from nonlinear periodic boundary value problems" Mathematica Japonica. 45(掲載決定). (1997)
[Publications] A.Tsutsumi: "On an application of hypoellipticity to solutions of functional equations" A equations Mathematicae. (掲載決定). (1996)
[Publications] T.Watanabe: "The Chern character of the symmetric space EI" Publications of the Research Institute for Math.Sciences. 31. 533-544 (1995)
[Publications] M.O'uchi: "A differentiable structure for a bundle of C^*-algebras associated with a dynamical system" Pacific Journal of Mathematics. 168. 291-311 (1995)

1995 Fiscal Year Annual Research Report

符号理論と組合せ論の研究

Principal Investigator

濱田 昇 大阪女子大学, 学芸学部, 教授 (90033844)

Research Products

[Publications] N.Hamada: "construction of some optimal ternary linear codes and the uniqueness of〔294,6,195;3〕-codes meeting the Griesmer bound" Finite Fields and Their Application. 1. 458-468 (1995)

[Publications] N.Hamada: "A characterization of some{3U_<μ+1>,3U_μ;k-1,q}-minihyper and some〔n,k,q^<k-1>-3q^μ;q〕-codes meeting the Griesmer bound" Discrete Mathematics. 146. 59-67 (1995)

[Publications] N.Hamada: "A characterization of some{31,9;4,3}-minihypers and some〔90,5,59;3〕-codes meeting the Griesmer bound" Mathematica Japonica. 41. 657-672 (1995)

[Publications] M.van Eupen,N.Hamada: "The nonexistence of ternary〔50,5,32〕codes" Designs,Codes and Cryptography. 7. 235-237 (1995)

[Publications] N.Hamada: "The nonexistence of some quaternary linear codes meeting the Griesmer bound and the bounds for n_4(5,d),1≦d≦256" Mathematica Japonica. 43. 7-21 (1996)

[Publications] N.Hamada: "A characterization of{43,13;4,3}-minihypers and projective ternary〔78,5,51;3〕-codes" Mathematica Japonica. 43. 253-266 (1996)

[Publications] N.Hamada: "A necessary and sufficient condition for the existence of some ternary〔n,k,d〕codes meeting the Griesmer bound" Designs,Codes and Cryptography. 8(印刷中). (1996)

[Publications] N.Hamada: "The nonexistence of〔71,5,46;3〕-codes" Journal of Statistical Planning and Inference. 50(印刷中). (1996)

[Publications] N.Hamada: "The nonexistence of some ternary linear codes of dimension 6 and the bounds for n_3(6,d),1≦d≦243" Mathematica Japonica. 43(印刷中). (1996)

[Publications] N.Hamada: "A characterization of some{25,7;3,3}-minihypers and some〔15,4,9;3〕-codes with B_2=0" Journal of Statistical Planning and Inference. 51(印刷中). (1996)

[Publications] N.Hamada: "The uniqueness of〔87,5,57;3〕-codes and the nonexistence of〔258,6,171;3〕-codes" Journal of Statistical Planning and Inference. 51(印刷中). (1996)

[Publications] N.Hamada: "The nonexistence of ternary〔231,6,153〕codes" Ars Combinatoria. (掲載決定). (1996)

[Publications] K.Ishihara: "On the optimum SOR iterations for finite difference approximation to periodic boundary value problems" Mathematica Japonica. 41. 199-209 (1995)

[Publications] K.Ishihara: "Optimum SOR iterations for finite difference equations arising from nonlinear periodic boundary value problems" Mathematica Japonica. 45(掲載決定). (1997)

[Publications] A.Tsutsumi: "On an application of hypoellipticity to solutions of functional equations" A equations Mathematicae. (掲載決定). (1996)

[Publications] T.Watanabe: "The Chern character of the symmetric space EI" Publications of the Research Institute for Math.Sciences. 31. 533-544 (1995)

[Publications] M.O'uchi: "A differentiable structure for a bundle of C^*-algebras associated with a dynamical system" Pacific Journal of Mathematics. 168. 291-311 (1995)

濱田昇大阪女子大学, 学芸学部, 教授 (90033844)