113
Views
15
CrossRef citations to date
0
Altmetric
Original Articles

Automorphisms and Equivalence of Bent Functions and of Difference Sets in Elementary Abelian 2-Groups

Pages 1077-1131 | Received 16 Nov 2004, Published online: 03 Sep 2006

REFERENCES

  • Alperin , J. ( 1979 ). Projective modules for SL(2, 2 n ) . J. Pure. Appl. Algebra 15 : 219 – 234 . [CSA]
  • Alperin , J. , Gorenstein , D. ( 1972 ). A vanishing theorem for cohomology . Proc. Amer. Mat. Soc. 32 ( 15 ): 87 – 88 . [CSA]
  • Artin , E. ( 1957 ). Geometric Algebra . Interscience .
  • Aschbacher , M. ( 1984 ). On the maximal subgroups of the finite classical groups . Invent. Math. 71 : 469 – 514 . [CSA] [CROSSREF]
  • Aschbacher , M. ( 2000 ). Finite Group Theory . Cambridge Univ. Press .
  • ATLAS of Finite Group Representations . http://for.mat.bham.ac.uk/atlas/ . Accessed January 25, 2006 .
  • Baumann , B. ( 1984 ). Symmetrische Singer-Zyklen über Körpern der Charakteristik 2 . Mitt. Math. Sem. Gießen 163 : 135 – 140 . [CSA]
  • Bell , G. ( 1978 ). Cohomology of degree 0, 1, and 2 of SL n (q) I–II . J. Algebra 54 : 216 – 238 , 239 – 259 . [CSA] [CROSSREF]
  • Bending , T. ( 1993 ). Bent Functions, SDP Designs and Their Automorphism Groups . Thesis, Queen Mary and Westfield College, Univ. London . [CSA]
  • Burkhardt , R. ( 1979 ). Über die Zerlegungszahlen der unitären Gruppen PSU(3, 22f ) . Jour. Alg. 61 : 548 – 581 . [CSA] [CROSSREF]
  • Charnes , C. , Dempwolff , U. ( 2000 ). The eight dimensional ovoids over GF(5) . Math. Computations 70 : 853 – 861 . [CSA] [CROSSREF]
  • Charnes , C. , Rötteler , M. , Beth , T. ( 2002 ). Homogeneous bent functions, invariants, and designs . Designs, Codes, Crypt. 26 : 139 – 154 . [CSA] [CROSSREF]
  • Charnes , C. , Rötteler , M. , Beth , T. ( 2003 ). On the sstabilizers of homogeneous bent functions in the affine group . In: 7th Finite Fields Symposium . Toulouse, France , May 2003 .
  • Conway , J. , Curtis , R. , Norton , S. , Parker , R. , Wilson , R. ( 1985 ). An Atlas of Finite Groups . Clarendon Press .
  • Cooperstein , B. ( 1981 ). Maximal subgroups of G2(2 n ) . J. Algebra 70 : 23 – 36 . [CSA] [CROSSREF]
  • Dempwolff , U. ( 1984 ). Linear groups with large cyclic subgroups and translation planes . Rend. Sem. Mat. Univ. Padova 77 : 69 – 113 . [CSA]
  • Dempwolff , U. ( 1988 ). A characterization of the generalized twisted field planes . Arch. Math. 50 : 477 – 480 . [CSA] [CROSSREF]
  • Dempwolff , U. ( 2004 ). Affine rank 3 groups on symmetric designs . Designs, Codes, Crypt. 31 : 159 – 168 . [CSA] [CROSSREF]
  • Dempwolff , U. , Reifart , A. ( 1983 ). The classification of the translation planes of order 16, I . Geom. Ded. 15 : 137 – 153 . [CSA]
  • Dieudonné, J. ( 1955 ). La Géométrie des Groups Classiques . Springer .
  • Dillon , J. ( 1972 ). A survey of bent functions . NSA Tech. J. NSAL-S-203, 092, Special Issue , 191 – 216 . [CSA]
  • Dillon , J. ( 1975 ). Elementary Hadamard difference sets . In: Proc. 6th S.E. Conf. Comb., Graph Theory and Computing . Utilitas Math. Boca Raton , pp. 237 – 249 .
  • GAP – Groups, Algorithms, and Programming, V4.2. The GAP group, Aachen, St. Andrews. www-gap.dcs.st-and.ac.uk. Accessed January 25, 2006 .
  • Griess , R. ( 1976 ). On a subgroup of order 215|GL(5,2)| in E 8(C), the Dempwolff group and Aut(D 8 ○ D 8 ○ D 8) . J. Alg. 40 : 271 – 279 . [CSA] [CROSSREF]
  • Grove , L. ( 2002 ). Classical Groups and Geometric Algebra . Grad. Stud. in Math . Vol. 39 . Amer. Math. Society .
  • Guralnik , R. , Penttila , T. , Praeger , C. , Saxl , J. ( 1999 ). Linear groups with orders having certain large prime divisors . Proc. Lond. Math. Soc. III Ser. 78 : 167 – 214 . [CSA] [CROSSREF]
  • Hering , C. ( 1974 ). Transitive linear groups and linear groups which contain irreducible subgroups of prime order I . Geom. Ded. 2 : 425 – 460 . [CSA]
  • Hering , C. ( 1985 ). Transitive linear groups and linear groups which contain irreducible subgroups of prime order II . J. Alg. 93 : 151 – 164 . [CSA] [CROSSREF]
  • Hou , X. ( 1998 ). Cubic bent functions . Discrete Math. 189 : 149 – 161 . [CSA] [CROSSREF]
  • Huppert , B. ( 1970 ). Singer-Zyklen in klassischen Gruppen . Math. Z. 117 : 141 – 150 . [CSA] [CROSSREF]
  • Huppert , B. , Blackburn , N. (1967/1982 ). Endliche Gruppen I and Finite Groups II–III . Springer .
  • Jansen , C. , Lux , K. , Parker , R. , Wilson , R. ( 1995 ). An Atlas of Brauer Characters . Clarendon Press .
  • Jones , W. , Parshall , B. ( 1975 ). On the 1-cohomology of finite groups of Lie type . In: Scott , W. , Gross , F. , eds. Proc. Conf. Finite Groups . Academic Press , pp. 313 – 327 .
  • Kantor , W. (1975). Symplectic groups, symmetric designs and line ovals. J. Alg. 33:43–58. [CSA] [CROSSREF]
  • Kantor , W. ( 1983 ). Exponential numbers of two weight codes, difference sets and symmetric designs . Discrete Math. 46 : 95 – 98 . [CSA] [CROSSREF]
  • Kantor , W. , Liebler , R. ( 1982 ). The rank 3 permutation representations of the finite classical groups . Trans. Amer. Math. Soc. 271 : 1 – 71 . [CSA]
  • Kleidman , P. ( 1988 ). The maximal subgroups of the Steinberg triality groups 3D4(q) and of their automorphism groups . J. Alg. 115 : 182 – 199 . [CSA] [CROSSREF]
  • Kleidman , P. , Liebeck , M. ( 1990 ). The Subgroup Structure of the Finite Classical Groups . Cambridge Univ. Press .
  • Landrock , P. ( 1983 ). Finite Group Algebras and Their Modules . Cambridge Univ. Press .
  • Liebeck , M. ( 1985 ). On the orders of maximal subgroups of finite classical groups . Proc. Lond. Math. Soc. 50 ( 3 ): 426 – 446 . [CSA]
  • Liebeck , M. ( 1987 ). The affine permutation groups of rank three . Proc. Lond. Math. Soc. 54 ( 3 ): 477 – 516 . [CSA]
  • Lüneburg , H. ( 1980 ). Translation Planes . Springer .
  • Mann , B. ( 1965 ). Difference sets in elementary Abelian groups . Ill. J. Math. 9 : 212 – 219 . [CSA]
  • McFarland , R. ( 1973 ). A family of noncyclic difference sets . J. Comb. Theory (A) 15 : 1 – 10 . [CSA] [CROSSREF]
  • McLaughlin , J. ( 1969 ). Some subgroups of SL n (F2) . Ill. J. Math. 13 : 108 – 115 . [CSA]
  • Modular Atlas Homepage . www.math.rwth-aachen.de/homes/MOC/ .
  • Oyama , T. ( 1985 ). On quasifields . Osaka J. Math. 22 : 35 – 54 . [CSA]
  • Rothaus , O. ( 1976 ). On “bent” functions . J. Comb. Theory (A) 20 : 300 – 305 . [CSA] [CROSSREF]
  • Seitz , G. , Zalesskii , A. ( 1993 ). On the minimal degree of projective representation of the finite Chevalley groups . J. Alg. 158 : 233 – 243 . [CSA] [CROSSREF]
  • Sin , P. ( 1992 ). On the 1-cohomology of the groups G2(2 n ) . Comm. Algebra 20 : 2653 – 2662 . [CSA]
  • Sin , P. ( 1996 ). Modular representations of the Hall-Janko group . Comm. Algebra 24 : 4513 – 4547 . [CSA]
  • The Magma Computational Algebra System . http://magma.maths.usyd.edu.au/magma/ . Accessed January 24, 2006 .
  • Wagner , A. ( 1976 ). The faithful linear representations of least degree of S n and A n over a field of characteristic 2 . Math. Z. 151 : 127 – 137 . [CSA] [CROSSREF]
  • Communicated by A. Turull.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.