Complete weight enumerators of generalized doubly-even self-dual codes

[1]  W. J. Harvey,et al.  TATA LECTURES ON THETA I (Progress in Mathematics, 28) , 1986 .

[2]  J. Wolfart.  Eine arithmetische Eigenschaft automorpher Formen zu gewissen nicht-arithmetischen Gruppen , 1983 .

[3]  W. Ebeling,et al.  Lattices and Codes: A Course Partially Based on Lectures by F. Hirzebruch , 1994 .

[4]  J. Sturm.  The critical values of zeta functions associated to the symplectic group , 1981 .

[5]  J. Lehman.  Levels of positive definite ternary quadratic forms , 1992 .

[6]  M. Harris.  Special values of zeta functions attached to Siegel modular forms , 1981 .

[7]  G. Frey,et al.  A remark concerning m -divisibility and the discrete logarithm in the divisor class group of curves , 1994 .

[8]  A simple proof of the modular identity for theta series , 2005 .

[9]  YoungJu Choie,et al.  The complete weight enumerator of type II codes over Z2m and Jacobi forms , 2001, IEEE Trans. Inf. Theory.

[10]  E. M. Rains,et al.  Self-Dual Codes , 2002, math/0208001.

[11]  David L. Winter,et al.  The automorphism group of an extraspecial $p$-group , 1972 .

[12]  Don Zagier,et al.  Heegner points and derivatives ofL-series , 1986 .

[13]  Masaaki Harada,et al.  Shadow lattices and shadow codes , 2000, Discret. Math..

[14]  Don B. Zagier,et al.  On singular moduli. , 1984 .

[15]  R. Schulze-Pillot.  Thetareihen positiv definiter quadratischer Formen , 1984 .

[16]  W. Couwenberg.  A simple proof of the modular identity for theta functions , 2003 .

[17]  Michio Ozeki.  On the notion of Jacobi polynomials for codes , 1997 .

[18]  M. Furusawa.  On Petersson norms for some liftings , 1984 .

[19]  N. J. A. Sloane,et al.  The Invariants of the Cli ord , 1999 .

[20]  N. M. Katz.  P-ADIC Properties of Modular Schemes and Modular Forms , 1973 .

[21]  W. Kohnen.  On the Petersson norm of a Siegel-Hecke Eigenform of degree two in the Maass space. , 1985 .

[22]  W. Kohnen.  Lifting modular forms of half-integral weight to Siegel modular forms of even genus , 2002 .

[23]  S. Dougherty,et al.  SHADOWS OF CODES AND LATTICES , 2002 .

[24]  N. J. A. Sloane,et al.  Generalizations of Gleason's theorem on weight enumerators of self-dual codes , 1972, IEEE Trans. Inf. Theory.

[25]  N. Sloane,et al.  A new upper bound for the minimum of an integral lattice of determinant 1 , 1990 .

[26]  Neal Koblitz,et al.  Hyperelliptic cryptosystems , 1989, Journal of Cryptology.

[27]  P. Lockhart.  On the discriminant of a hyperelliptic curve , 1994 .

[28]  Koichi Betsumiya.  The Type II Property for Self-Dual Codes over Finite Fields of Characteristic Two , 2002 .

[29]  W. Kohnen,et al.  Special values of modular functions on Hecke groups , 2003 .

[30]  Patrick Solé,et al.  Type II Codes Over F 4 + uF 4 . , 2001 .

[31]  Eiichi Bannai,et al.  On the Ring of Simultaneous Invariants for the Gleason-MacWilliams Group , 1999, Eur. J. Comb..

[32]  F. MacWilliams,et al.  The Theory of Error-Correcting Codes , 1977 .

[33]  B. M. Fulk.  MATH , 1992 .

[34]  Michel Broué,et al.  Polynômes des poids de certains codes et fonctions thêta de certains réseaux , 1972 .

[35]  R. Borcherds.  Automorphic forms onOs+2,2(R) and infinite products , 1995 .

[36]  T. Ibukiyama.  On Jacobi Forms and Siegel Modular Forms of Half Integral Weights , 1992 .

[37]  S. Böcherer.  Über Funktionalgleichungen automorpher L-Funktionen zur Siegelschen Modulgruppe. , 1985 .

[38]  N. Koblitz.  Elliptic curve cryptosystems , 1987 .

[39]  G. Nebe.  Self-dual codes and invariant theory 1 , 2022 .

[40]  Alfred Menezes,et al.  Isomorphism Classes of Genus-2 Hyperelliptic Curves Over Finite Fields , 2002, Applicable Algebra in Engineering, Communication and Computing.

[41]  Patrick Solé,et al.  Self-dual codes over Z~4 and half-integral weight modular forms , 2002 .

[42]  N. J. A. Sloane,et al.  Sphere Packings, Lattices and Groups , 1987, Grundlehren der mathematischen Wissenschaften.

[43]  Eine Invarianzgruppe für die vollständige Gewichtsfunktion selbstdualer Codes , 1989 .

[44]  K. Takeuchi.  Arithmetic triangle groups , 1977 .

[45]  E. Hecke,et al.  Über die Bestimmung Dirichletscher Reihen durch ihre Funktionalgleichung , 1936 .

[46]  Paulo S. L. M. Barreto,et al.  Efficient Algorithms for Pairing-Based Cryptosystems , 2002, CRYPTO.

[47]  Steven T. Dougherty,et al.  Complete joint weight enumerators and self-dual codes , 2003, IEEE Trans. Inf. Theory.

[48]  Á. Seress,et al.  A mass formula for Type II codes over finite fields of characteristic two , 2002 .

[49]  G. Shimura.  The critical values of certain zeta functions associated with modular forms of half-integral weight , 1981 .

[50]  J. Lehner.  Discontinuous Groups and Automorphic Functions , 1964 .

[51]  Alain Robert,et al.  Introduction to modular forms , 1976 .

[52]  A. Andrianov,et al.  ON THE ANALYTIC PROPERTIES OF STANDARD ZETA FUNCTIONS OF SIEGEL MODULAR FORMS , 1979 .

[53]  D. Zagier.  Modular forms whose fourier coefficients involve zeta-functions of quadratic fields , 1977 .

[54]  Heinz Georg Quebbemann.  On even codes , 1991, Discret. Math..

[55]  Gabriel Cardona,et al.  Curves of genus two over fields of even characteristic , 2002 .

[56]  Shin-ichiro Mizumoto,et al.  Poles and residues of standardL-functions attached to Siegel modular forms , 1991 .

[57]  T. Gulliver,et al.  Type II Self-Dual Codes over Finite Rings and Even Unimodular Lattices , 1997 .

[58]  Fernando Q. Gouvêa.  Non-Ordinary Primes: A Story , 1997, Exp. Math..

[59]  W. Fischer,et al.  Sphere Packings, Lattices and Groups , 1990 .

[60]  C. Ziegler,et al.  Jacobi forms of higher degree , 1989 .

[61]  R. Rankin.  The Scalar Product of Modular Forms , 1952 .

[62]  Masaaki Harada,et al.  Type II Codes, Even Unimodular Lattices, and Invariant Rings , 1999, IEEE Trans. Inf. Theory.

[63]  Christine Bachoc,et al.  Type II codes over Z4 , 1997, IEEE Trans. Inf. Theory.

[64]  Eiichi Bannai,et al.  Construction of Jacobi forms from certain combinatorial polynomials , 1996 .

[65]  A. Andrianov.  THE MULTIPLICATIVE ARITHMETIC OR SIEGEL MODULAR FORMS , 1979 .

[66]  Michael J. Razar,et al.  Modular forms for ₀() and Dirichlet series , 1977 .

[67]  H. Niederreiter,et al.  Finite Fields: Encyclopedia of Mathematics and Its Applications. , 1997 .

[68]  Andrew M. Gleason,et al.  WEIGHT POLYNOMIALS OF SELF-DUAL CODES AND THE MacWILLIAMS IDENTITIES , 1970 .

[69]  G. Shimura.  On the Holomorphy of Certain Dirichlet Series , 1975 .

[70]  M. Kerimov.  The theory of error-correcting codes☆ , 1980 .

[71]  W. Eholzer,et al.  Product expansions of conformal characters , 1996, hep-th/9607165.

[72]  J. Raleigh.  On the Fourier coefficients of triangle functions , 1962 .

[73]  Haruzo Hida,et al.  Galois representations into GL2 (Zp[[X]]) attached to ordinary cusp forms , 1986 .

[74]  Jacques Wolfmann,et al.  A class of doubly even self dual binary codes , 1985, Discret. Math..

[75]  S. Böcherer.  Über die Fourier-Jacobi-Entwicklung Siegelscher Eisensteinreihen II , 1983 .

[76]  W. Kohnen,et al.  The arithmetic of the values of modular functions and the divisors of modular forms , 2004, Compositio Mathematica.

[77]  Eiichi Bannai,et al.  Modular invariance property of association schemes, type II codes over finite rings and finite abelian groups and reminiscences of François Jaeger (a survey) , 1999 .

[78]  Jay A. Wood.  Duality for modules over finite rings and applications to coding theory , 1999 .

[79]  Koichi Betsumiya,et al.  Codes over F4, Jacobi forms and Hilbert-Siegel modular forms over Q(sqrt(5)) , 2005, Eur. J. Comb..

[80]  Bernhard Liehl,et al.  On the group S L 2 over orders of arithmetic type. , 1981 .

[81]  P. Stevenhagen,et al.  ELLIPTIC FUNCTIONS , 2022 .

[82]  Akihiro Munemasa,et al.  On type II codes over F4 , 2001, IEEE Trans. Inf. Theory.

[83]  W. Kohnen,et al.  Special values of elliptic functions at points of the divisors of Jacobi forms , 2003 .

[84]  G. C. Shephard,et al.  Finite Unitary Reflection Groups , 1954, Canadian Journal of Mathematics.

[85]  Jonathan M. Borwein,et al.  A cubic counterpart of Jacobi’s identity and the AGM , 1991 .

[86]  B. R. McDonald.  Finite Rings With Identity , 1974 .

[87]  G. Pasquier.  Binary Self Dual Codes Construction from Self Dual Codes Over a Galois Field F2m , 1983 .

[88]  Jonathan M. Borwein,et al.  Cubic Analogues Of The Jacobian Theta Function , 1993 .

[89]  Yingpu Deng,et al.  Isomorphism classes of hyperelliptic curves of genus 3 over finite fields , 2006, Finite Fields Their Appl..