메뉴 건너뛰기




Volumn 49, Issue 3, 1999, Pages 763-782

Modular invariance property of association schemes, type ii codes over finite rings and finite abelian groups, and reminiscences of françois jaeger (a survey)

Author keywords

Association scheme; Code over finite ring; Hermitian modular form; Modular invariance; Spin model; Type II code

Indexed keywords


EID: 0033444417     PISSN: 03730956     EISSN: None     Source Type: Journal    
DOI: 10.5802/aif.1690     Document Type: Article
Times cited : (9)

References (49)
  • 1
    • 0031123901 scopus 로고    scopus 로고
    • Applications of coding theory to the construction of modular lattices
    • C. BACHOC, Applications of coding theory to the construction of modular lattices, J. Combinatorial Theory, (A) 78 (1997), 173-187.
    • (1997) J. Combinatorial Theory, (A) , vol.78 , pp. 173-187
    • Bachoc, C.1
  • 2
    • 0011672740 scopus 로고
    • Association schemes and fusion algebras
    • E. BANNAI, Association schemes and fusion algebras (an introduction), J. Algebraic Combinatorics, 2 (1993), 327-344.
    • (1993) J. Algebraic Combinatorics , vol.2 , pp. 327-344
    • Bannai, E.1
  • 3
    • 0040119936 scopus 로고    scopus 로고
    • Invariant rings of finite groups and automorphic forms
    • Yamagata University, July 24-27, 1996
    • E. BANNAI, Invariant rings of finite groups and automorphic forms (a survey) (in Japanese), Algebra Symposium Proceedings (at Yamagata University, July 24-27, 1996), 42 (1996), 173-187.
    • (1996) Algebra Symposium Proceedings , vol.42 , pp. 173-187
    • Bannai, E.1
  • 4
    • 38149147036 scopus 로고
    • Modular invariance of the character table of the Hamming association scheme H (d, q)
    • E. BANNAI and E. BANNAI, Modular invariance of the character table of the Hamming association scheme H (d, q), J. Number Theory, 57 (1994), 79-92.
    • (1994) J. Number Theory , vol.57 , pp. 79-92
    • Bannai, E.1    Bannai, E.2
  • 5
    • 0001826014 scopus 로고
    • Generalized spin models and association schemes
    • Ser (A)
    • E. BANNAI and E. BANNAI, Generalized spin models and association schemes, Memoire of Fac. Sci. Kyushu University, Ser (A), 47 (1993), 379-409.
    • (1993) Memoire of Fac. Sci. Kyushu University , vol.47 , pp. 379-409
    • Bannai, E.1    Bannai, E.2
  • 12
    • 21344447468 scopus 로고    scopus 로고
    • Construction of jacobi forms from certain combinatorial polynomials
    • E. BANNAI and M. OZEKI, Construction of Jacobi forms from certain combinatorial polynomials, Proc. Japan Acad. (A), 72 (1996), 12-15.
    • (1996) Proc. Japan Acad. (A) , vol.72 , pp. 12-15
    • Bannai, E.1    Ozeki, M.2
  • 13
    • 0040119935 scopus 로고    scopus 로고
    • Duality maps of finite abelian groups and their applications to spin models
    • Etsuko BANNAI and A. MUNEMASA, Duality maps of finite abelian groups and their applications to spin models, J. Algebraic Combinatorics, 8 (1998), 223-234.
    • (1998) J. Algebraic Combinatorics , vol.8 , pp. 223-234
    • Bannai, E.1    Munemasa, A.2
  • 15
    • 0001004462 scopus 로고
    • Polynômes des poids de certains codes et fonctions theta de certains réseaux
    • M. BROUÉ and M. ENGUEHARD, Polynômes des poids de certains codes et fonctions theta de certains réseaux, Ann. Sci. Ecole Norm. Sup., 5 (1972), 157-181.
    • (1972) Ann. Sci. Ecole Norm. Sup. , vol.5 , pp. 157-181
    • Broué, M.1    Enguehard, M.2
  • 18
    • 85041979556 scopus 로고
    • An algebraic approach to the association schemes of coding theory
    • P. DELSARTE, An algebraic approach to the association schemes of coding theory, Philips Research Reports Supplments, 10 (1973), 125-136.
    • (1973) Philips Research Reports Supplments , vol.10 , pp. 125-136
    • Delsarte, P.1
  • 21
    • 84963057467 scopus 로고
    • On codes and Siegel modular forms
    • W. DUKE, On codes and Siegel modular forms, International Math. Res. Notes, (1993), 125-136.
    • (1993) International Math. Res. Notes , pp. 125-136
    • Duke, W.1
  • 22
    • 0004171614 scopus 로고
    • a course partially based on lectures by F. Hirzebruch, Vieweg
    • W. EBELING, Lattices and Codes, a course partially based on lectures by F. Hirzebruch, Vieweg, 1994.
    • (1994) Lattices and Codes
    • Ebeling, W.1
  • 25
    • 0002762280 scopus 로고
    • Modulformen zweiten grades zum rationalen und gausssehen zahlkorper
    • E. FREITAG, Modulformen zweiten Grades zum rationalen und Gausssehen Zahlkorper, Sitzungsber. Heidelberg Akad. Wiss., 1967, 3-49.
    • (1967) Sitzungsber. Heidelberg Akad. Wiss. , pp. 3-49
    • Freitag, E.1
  • 27
    • 0001298679 scopus 로고
    • Weight polynomials of self-dual codes and the MacWilliams identities
    • A. M. GLEASON, Weight polynomials of self-dual codes and the MacWilliams identities, Actes Congrès Intern. Math., 3 (1970), 211-215.
    • (1970) Actes Congrès Intern. Math. , vol.3 , pp. 211-215
    • Gleason, A.M.1
  • 29
    • 0001057094 scopus 로고
    • On siegel modular forms of genus 2, (1) and (II)
    • J. IGUSA, On Siegel modular forms of genus 2, (1) and (II), Amer. J. Math., 84, 88 (1962) (1966), 175-200, 221-236.
    • (1962) Amer. J. Math. , vol.84-88 , pp. 175-200
    • Igusa, J.1
  • 30
    • 0002245009 scopus 로고
    • Strongly regular graphs and spin models for the kauffman polynomial
    • F. JAEGER, Strongly regular graphs and spin models for the Kauffman polynomial, Geomet. Dedicata, 44 (1992), 23-52.
    • (1992) Geomet. Dedicata , vol.44 , pp. 23-52
    • Jaeger, F.1
  • 31
    • 0039528405 scopus 로고
    • Spin models for link invariants
    • "Survey in Combinatorics, 1995", London Math. Soc.
    • F. JAEGER, Spin models for link invariants, in "Survey in Combinatorics, 1995", London Math. Soc., Lecture Notes Series, 218 (1995), 71-101.
    • (1995) Lecture Notes Series , vol.218 , pp. 71-101
    • Jaeger, F.1
  • 32
    • 0038935817 scopus 로고    scopus 로고
    • Towards a classification of spin models in terms of association schemes
    • Progress in Algebraic Combinatorics
    • F. JAEGER, Towards a classification of spin models in terms of association schemes, in Progress in Algebraic Combinatorics, Advanced Studies in Pure Math., 24 (1996), 197-225.
    • (1996) Advanced Studies in Pure Math. , vol.24 , pp. 197-225
    • Jaeger, F.1
  • 33
    • 0002919154 scopus 로고    scopus 로고
    • Bose-mesner algebras related to type II matrices and spin models
    • F. JAEGER, M. MATSUMOTO and K. NOMURA, Bose-Mesner algebras related to Type II matrices and spin models, J. Algebraic Combinatorics, 8 (1998), 39-72.
    • (1998) J. Algebraic Combinatorics , vol.8 , pp. 39-72
    • Jaeger, F.1    Matsumoto, M.2    Nomura, K.3
  • 34
    • 0002450607 scopus 로고
    • Uber den dualitatssatz der charactere nichtcommutativer gruppen
    • Y. KAWADA, Uber den Dualitatssatz der Charactere nichtcommutativer Gruppen, Proc. Phys, Math. Soc. Japan, 24 (1942), 97-109.
    • (1942) Proc. Phys, Math. Soc. Japan , vol.24 , pp. 97-109
    • Kawada, Y.1
  • 35
    • 0003310843 scopus 로고
    • Modular forms on half-spaces of quaternions
    • A. KRIEG, Modular Forms on Half-Spaces of Quaternions, Springer Lecture Note Series, 1143 (1985).
    • (1985) Springer Lecture Note Series , vol.1143
    • Krieg, A.1
  • 38
    • 0010139382 scopus 로고    scopus 로고
    • A note on the structure of the ring of symmetric hermitian modular forms of degree 2 over the Gaussian field
    • S. NAGAOKA, A note on the structure of the ring of symmetric Hermitian modular forms of degree 2 over the Gaussian field, J. Math. Soc. Japan, 48 (1996), 525-549.
    • (1996) J. Math. Soc. Japan , vol.48 , pp. 525-549
    • Nagaoka, S.1
  • 39
    • 0000884829 scopus 로고
    • Spin models constructed from hadamard matrices
    • K. NOMURA, Spin models constructed from Hadamard matrices, J. Combinatorial Theory (A), 68 (1994), 251-261.
    • (1994) J. Combinatorial Theory (A) , vol.68 , pp. 251-261
    • Nomura, K.1
  • 40
    • 0040713682 scopus 로고    scopus 로고
    • An algebra associated with a spin model
    • K. NOMURA, An algebra associated with a spin model, J. Algebraic Combinatorics, 6 (1997), 53-58.
    • (1997) J. Algebraic Combinatorics , vol.6 , pp. 53-58
    • Nomura, K.1
  • 41
    • 85033970649 scopus 로고    scopus 로고
    • Spin models and bose-mesner algebras
    • to appear
    • K. NOMURA, Spin models and Bose-Mesner algebras, Europ. J. Comb., (to appear).
    • Europ. J. Comb.
    • Nomura, K.1
  • 42
    • 0007546876 scopus 로고    scopus 로고
    • The dimension formula for the ring of code polynomials in genus 4
    • M. OURA, The dimension formula for the ring of code polynomials in genus 4, Osaka J. Math., 34 (1997), 53-72.
    • (1997) Osaka J. Math. , vol.34 , pp. 53-72
    • Oura, M.1
  • 43
    • 33748734063 scopus 로고    scopus 로고
    • On the notion of Jacobi polynomials for codes
    • M. OZEKI, On the notion of Jacobi polynomials for codes, Math. Proc. Cambridge Phil. Soc., 121 (1997), 15-30.
    • (1997) Math. Proc. Cambridge Phil. Soc. , vol.121 , pp. 15-30
    • Ozeki, M.1
  • 44
    • 84961485640 scopus 로고
    • On siegel modular forms, part I
    • B. RUNGE, On Siegel modular forms, part I, J. reine angew. Math., 436 (1993), 57-85.
    • (1993) J. Reine Angew. Math. , vol.436 , pp. 57-85
    • Runge, B.1
  • 45
    • 0038935818 scopus 로고
    • Theta functions and Siegel-Jacobi forms
    • B. RUNGE, Theta functions and Siegel-Jacobi forms, Acta Mathematica, 175 (1995), 165-196.
    • (1995) Acta Mathematica , vol.175 , pp. 165-196
    • Runge, B.1
  • 46
    • 0001253686 scopus 로고
    • Finite unitary reflection groups
    • G. C. SHEPHARD and J. A. TODD, Finite unitary reflection groups, Canad. J. Math., 6 (1954), 274-304.
    • (1954) Canad. J. Math. , vol.6 , pp. 274-304
    • Shephard, G.C.1    Todd, J.A.2
  • 47
    • 0040119934 scopus 로고
    • A matrix equation for association schemes
    • D. STANTON, A matrix equation for association schemes, Graphs and Combinatorics, 11 (1995), 103-108.
    • (1995) Graphs and Combinatorics , vol.11 , pp. 103-108
    • Stanton, D.1
  • 48
    • 0000149039 scopus 로고
    • On siegel modular forms of degree three
    • S. TSUYUMINE, On Siegel modular forms of degree three, Amer. J. Math., 108 (1986), 755-862.
    • (1986) Amer. J. Math. , vol.108 , pp. 755-862
    • Tsuyumine, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.