Top CV Research Lectures Links

Motoko Kawakita's Research

Research Interest

I am researching on algebraic curves over finite fields with many rational points and their applications to coding theory and cryptography.

Papers

  1. Generalised Howe curves of genus five attaining the Serre bound, arXiv:2412.03071.
  2. New sextics of genus 6 and 10 attaining the Serre bound (with A. Iezzi, M. Timpanella), Advances in Geometry 24(1) (2024), 99-109.
  3. An Fp2-maximal Wiman sextic and its automorphisms (with M. Giulietti, S. Lia, M. Montanucci), Advances in Geometry 21(4) (2021), 451-461.
  4. New examples of maximal curves with low genus (with D. Bartoli, M. Giulietti, M. Montanucci), Finite Fields and Their Applications 68 (2020), Article 101744.
  5. Some sextics of genera five and seven attaining the Serre bound, Lecture Notes in Computer Science 11321 (2018), 264--271.
  6. Wiman's and Edge's sextic attaining Serre's bound, European Journal of Mathematics 4 (2018), 330--334.
  7. Certain sextics with many rational points, Advances in Mathematics of Communications 11 (2017), no. 2, 289-292.
  8. Wiman's and Edge's sextic attaining Serre's bound II, Contemporary Mathematics 637 (2015), 191--203.
  9. On quotient curves of the Fermat curve of degree twelve attaining the Serre bound, International Journal of Mathematics 20 (2009), no. 5, 529--539.
  10. On certain subcovers of the Hermitian curve (with A. Garcia, S. Miura), Communications in Algebra 34 (2006), no. 3, 973--982.
  11. A quotient curve of the Fermat curve of degree twelve attaining the Serre bound, Journal of Algebra and Its Applications 4 (2005), 173--178.
  12. A quotient curve of the Fermat curve of degree twenty-three attaining the Serre bound, Journal of Pure and Applied Algebra 196 (2005), 101--110.
  13. On the distribution of linear codes (with T. Katsura), Natural Science Report of the Ochanomizu University 55 (2004), no. 2, 33--39.
  14. Kummer curves and their fibre products with many rational points, Applicable Algebra in Engineering, Communication and Computing 14 (2003), 55--64.
  15. Quadratic forms, fibre products and some plane curves with many points (with S. Miura), Acta Arithmetica 105 (2002), 371--386.
  16. Some explicit curves of genus three over finite fields of characteristic two with many rational points, Proceedings of the Second ISAAC Congress, Kluwer Academic Publishers (2000), 1171--1177.

Proceedings

  1. Computer search for curves with many points among certain quotient curves of the Fermat curves, 滋賀医科大学基礎学研究 15 (2014), 1--4.
  2. 代数幾何符号のための代数曲線論, 数理解析研究所講究録 1752 「諸分野との協働による数理科学のフロンティア」(2011), 3--6.
  3. On quotient curves of the Fermat curve of degree twelve attaining the Serre bound, 第五回代数曲線論シンポジウム報告集(2007), 13--17.
  4. On quotient curves of the Fermat curves attaining the Serre bound, 第6回「代数幾何・数論及び符号・暗号」研究集会報告集 (2006), 3--4.
  5. Some quotient curves of Fermat curves attaining Serre bound, 数理解析研究所講究録 1361 「符号と暗号の代数的数理」(2004), 47--50.
  6. Curves attaining Serre bound, 2003代数曲線論シンポジウム記録 (2003), 8--11.
  7. Methods of finding curves with many points, Proceedings of the fifth conference on algebraic geometry, number theory, coding theory and cryptography (2003), 55--65.
  8. Kummer curves with many rational points, Proceedings of the 8th Rhine Workshop on Computer Algebra (2002), 31--51.
  9. 符号と多数の有理点を持つ曲線について, 第3回「代数幾何・数論及び符号・暗号」研究集会報告集 (2000), 67--73.

Talks

  1. Some sextics of genera five and seven attaining the Serre bound, International Workshop on the Arithmetic of Finite Fields (WAIFI2018), ノルウェー・University of Bergen, 2018年6月.
  2. Certain sextics with many rational points, Workshop on Mathematics in Communications (WMC2016), スペイン・University of Cantabria, 2016年7月.
  3. On certain sextics with many rational points, Workshop on Galois point and related topics, 神奈川大学, 2015年9月.
  4. Certain sextics with many rational points, Workshop on the Occasion of Harald Niederreiter's 70th Birthday: Applications of Algebra and Number Theory, オーストリア・Johann Radon Institute for Computational and Applied Mathematics, 2014年6月.
  5. Wiman's and Edge's sextic attaining Serre's bound, Workshop around Algebraic Combinatorics, 高知大学, 2014年1月.
  6. Wiman's and Edge's sextic attaining Serre's bound, Arithmetic, Geometry, Cryptography and Coding Theory, フランス・Centre International de Rencontres Mathématiques, 2013年6月.
  7. 安全・高速な情報通信のための代数曲線論, JST数学領域 第4回領域シンポジウム「越境する数学」, 東京大学, 2012年11月.
  8. Wiman's and Edge's sextic attaining Serre's bound, Mini Workshop on Algebraic Curves for Coding Theory and Cryptography, 滋賀医科大学, 2012年7月.
  9. 代数幾何符号のための代数曲線論, 諸分野との協働による数理科学のフロンティア, 京都大学, 2010年11月.
  10. On quotient curves of the Fermat curve of degree twelve attaining the Serre bound, 第五回代数曲線論シンポジウム, 徳島大学, 2007年11月.
  11. On quotient curves of the Fermat curve of degree twelve attaining the Serre bound, 大阪市大COE京大COE若手合同発表会, 大阪市立大学, 2007年7月.
  12. Curves with many rational points and algebro-geometric codes, 台湾・National Center for Theoretical Sciences, 2007年7月.
  13. Curves with many rational points and algebro-geometric codes, 京都大学数理解析研究所談話会, 京都大学, 2007年6月.
  14. On quotient curves of the Fermat curve of degree 12 attaining the Serre bound, 中央大学モジュライセミナー, 中央大学, 2007年5月.
  15. On quotient curves of the Fermat curves attaining the Serre bound, 第6回「代数幾何・数論及び符号・暗号」研究集会, 東京大学, 2006年1月.
  16. Curves with many rational points, 合衆国・Institute for Advanced Study, 2004年10月.
  17. Constructing certain maximal curves from additive polynomials, 応用数理学会第12回「数論アルゴリズムとその応用」シンポジウム, キャンパスプラザ京都, 2004年7月.
  18. Curves attaining Serre bound, 第1回「代数曲線論」シンポジウム, 神奈川大学, 2003年12月.
  19. Some quotient curves of Fermat curves attaining Serre bound, 研究集会「符号と暗号の代数的数理」, 京都大学, 2003年11月.
  20. Methods of finding curves with many points, 第5回「代数幾何・数論及び符号・暗号」研究集会, 東京大学, 2003年1月.
  21. Algebraic curves with many rational points and application to coding theory, the 9th NS Forum, 国際基督教大学, 2002年12月.
  22. Kummer curves with many rational points, the 8th Rhine Workshop on Computer Algebra, ドイツ・Mannheim大学, 2002年3月.
  23. Kummer curves with many rational points, 応用数理学会 第6回「数論アルゴリズムとその応用」シンポジウム, お茶の水女子大学, 2002年1月.
  24. Quadratic forms, fibre products and some plane curves with many points, 熱海ワークショップ2001「代数幾何と符号理論」, ホテル西山, 2001年2月.
  25. Quadratic forms, fibre products and some plane curves with many points, 情報理論とその応用学会「代数曲線の数理と符号・暗号への応用」シンポジウム, 東京大学, 2001年1月. (三浦晋示氏との共同講演)
  26. 代数体を用いたある暗号方式のKASHを用いた実装について, 応用数理学会 第2回「数論アルゴリズムとその応用」シンポジウム, 中央大学, 2000年10月. (内山成憲氏,岡本龍明氏との共同講演)
  27. Some explicit curves of genus four over finite fields of characteristic two with many points, International Symposium on Applied Mathematics, 中国・大連理工大学, 2000年8月.
  28. Codes and curves over finite fields with many points, 第3回「代数幾何・数論及び符号・暗号」研究集会, 東京大学, 2000年1月.
  29. Some explicit curves of genus three over finite fields of characteristic two with many rational points, International Society for Analysis, its Applications and Computation, 福岡工業大学, 1999年8月.