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Structure of a code related to Sp(4, q), q even

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Abstract

We determine the socle and the radical series of the binary code associated with a finite regular generalized quadrangle of even order, considered as a module for the commutator of each of the orthogonal subgroups in the corresponding symplectic group.

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References

  1. Alperin J L, Projective modules for SL(2, 2n), J. Pure Appl. Algebra 15 (1979) 219–234

    Article  MATH  MathSciNet  Google Scholar 

  2. Dembowski P, Finite geometries, Classics in Mathematics (Berlin: Springer-Verlag) (1997) (reprint of 1968 edition)

    Google Scholar 

  3. Dye R H, Interrelations of symplectic and orthogonal groups in characteristic two, J. Algebra 59 (1979) 202–221

    Article  MATH  MathSciNet  Google Scholar 

  4. Dye R H, On the Arf invariant, J. Algebra 53 (1978) 36–39

    Article  MATH  MathSciNet  Google Scholar 

  5. Flesner D E, The geometry of subgroups of P Sp 4(2n), Illinois J. Math. 19 (1975) 48–70

    MATH  Google Scholar 

  6. Flesner D E, Maximal subgroups of P Sp 4(2n), containing central elations or noncentered skew elations, Illinois J. Math. 19 (1975) 247–268

    MATH  MathSciNet  Google Scholar 

  7. Hirschfeld J W P, Finite projective spaces of three dimensions (Oxford: Oxford University Press) (1985)

    MATH  Google Scholar 

  8. Hirschfeld J W P, Projective geometries over finite fields (Oxford: Oxford University Press) (1998)

    MATH  Google Scholar 

  9. Huppert B and Blackburn N, Finite groups (Berlin: Springer-Verlag) (1982) vol. 2

    Google Scholar 

  10. Jones A, Integral representations of direct product of groups, Canad. J. Math. 15 (1963) 625–630

    MATH  MathSciNet  Google Scholar 

  11. Lang S, Algebra, Third edition (New York: Addison-Wessley) (1999)

    Google Scholar 

  12. Payne S E and Thas J A, Finite generalized quadrangles (Boston: Advance Publishing Program, Pitman) (1984)

    MATH  Google Scholar 

  13. Sastry N S N, Codes and generalized polygons, in: Proc. of Seminar on combinatorics and applications in honour of Prof. S S Shrikhande (Calcutta: Indian Statistical Institute) (1982) pp. 303–310

    Google Scholar 

  14. Sastry N S N and Sin P, The code of regular generalized quadrange of even order, Proc. Symp. Pure Math. 63 (1998) 485–496

    MathSciNet  Google Scholar 

  15. Sastry N S N and Sin P, The binary code associated with nondegenerate quadrics of a symplectic space of even order, J. Combin. Theory (A) 94 (2001), 1–14

    Article  MATH  Google Scholar 

  16. Sastry N S N and Sin P, On the doubly transitive permutation representations of Sp(2n, F2), J. Algebra 257 (2002) 509–527

    Article  MATH  MathSciNet  Google Scholar 

  17. Sin P, Extension of simple modules for Sp 4(2n) and Sz(2n), Bull. London Math. Soc. 24 (1992) 159–164

    Article  MATH  MathSciNet  Google Scholar 

  18. Steinberg R, Representations of Algebraic groups, Nagoya J. Math. 22 (1963) 33–56

    MATH  MathSciNet  Google Scholar 

  19. Steinberg R, Lectures on Chevalley Groups, Mimeographed Notes (New Haven, Conn.: Yale Univ. Math. Dept) (1968)

    Google Scholar 

  20. Taylor D E, The geometry of the classical groups, sigma series in pure mathematics (Berlin: Helderman-Verlag (1992) vol. 9

    Google Scholar 

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Correspondence to N. S. Narasimha Sastry.

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Sastry, N.S.N., Shukla, R.P. Structure of a code related to Sp(4, q), q even. Proc Math Sci 117, 457–470 (2007). https://doi.org/10.1007/s12044-007-0038-5

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  • DOI: https://doi.org/10.1007/s12044-007-0038-5

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