Lectures on Galois Geometries and Steiner Systems

  • G. Tallini
Part of the International Centre for Mechanical Sciences book series (CISM, volume 313)


The pager consists of four lectures held at “Centre International des Sciences Meccaniques” of Udine (Italy), June 1989. Their content is the following. General concepts on Galois geometry and Steiner systems. The theory of h-sets in Steiner systems, with particular attention to Galois spaces. The theory of blocking sets, the even and odd type sets in a Steiner system. Applications to linear error correcting codes.


Linear Code Linear Error Steiner System Finite Geometry Partial Spread 


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  1. [1]
    A. Beutelspacher, Blocking sets and partial spreads in finite projective spaces, Math. Z., 145 (1975), 211–229.CrossRefMATHMathSciNetGoogle Scholar
  2. [2]
    A.A. Bruen, Baer subplane and blocking set, Bull. Amer. Math. Soc., 76 (1970), 342–344.CrossRefMATHMathSciNetGoogle Scholar
  3. [3]
    A.A. Bruen, Blocking sets in projective planes, Siam. J. Appl. Math. 3 (1971), 380–392.CrossRefMathSciNetGoogle Scholar
  4. [4]
    A.A. 3ruen and J.A. Thas, Blocking sets, Geometriae Dedicata, 6 (1977), 193–203.MathSciNetGoogle Scholar
  5. [5]
    P.J. Cameron and J.H. van Lint, Graph theory, coding theory and block designs, L M S Lecture Note Series 19, 1975, Cambridge Univ. Press.Google Scholar
  6. [6]
    P.V. Ceccherini, G. Tallini, Codes, caps and linear spaces, Finite geometries and designs, Proc. of the second Isle of Thorns Conference 1980, London Math. Soc. Lecture Note Series 49, Cambridge Univ. Press 1981.Google Scholar
  7. [7]
    P.V. Ceccherini, G. Tallini, Caps related to incidence structures and to linear codes, Annals of Discrete Math., North Holland Publ. Co. 14 (1982) 175–182.CrossRefMATHMathSciNetGoogle Scholar
  8. [8]
    P. Dembowsky, Finite geometries, Ergebnisse der Math. Springer, Berlin, 1968.Google Scholar
  9. [9]
    J. Doyen, A. Rosa, An updated bibliography and survey of Steiner systems, Annals of Discrete Math., 7 (1980), 317–349.CrossRefMATHMathSciNetGoogle Scholar
  10. [10]
    J.W.P. Hirschfeld, Projective Geometries over Finite Fields, Clarendon Press, Oxford (1979).MATHGoogle Scholar
  11. [11]
    F.J. Mac Williams, N.J.A. Sloane, The theory of Error-correcting Codes, North Holland Publ. Co. Amsterdam, New York, Oxford (1977).Google Scholar
  12. [12]
    F. Mazzocca, G. Tallini, On the non existence of blocking sets in PG(n,q) and AG(n,q) for all large enough n, Simon Stevin 1 (1985), 43–50.MathSciNetGoogle Scholar
  13. [13]
    B. Segre, Ovals in a finite projective plane, Canad. J. Math., 7 (1955) 415–416.MathSciNetGoogle Scholar
  14. [14]
    B. Segre, Curve razionali normali e k-archi neoli spazi finiti, Ann. Mat. pura appl. (4) 39 (1955) 357–379.CrossRefMATHMathSciNetGoogle Scholar
  15. [15]
    B. Segre, Le geometrie di Galois, Ann. Mat. (4) 48 (1959) 1–97.CrossRefMATHMathSciNetGoogle Scholar
  16. [16]
    B. Segre, Introduction to Galois geometries, MeT. Acc. Naz. Lincei, (8) 8 (1967) 133–236.MATHMathSciNetGoogle Scholar
  17. [17]
    G. Tallini, Le geometrie di Galois e le loro applicazioni alla statistica e alla teoria dell’informazione, Rend. Mat. 19 (1960) 379–400.MathSciNetGoogle Scholar
  18. [18]
    G. Tallini, On caps of kind s in a Galois r-dimensional space, Acta Aritho. VII (1961) 19–28.MathSciNetGoogle Scholar
  19. [19]
    G. Tallini, Un’applicazione della geometria di Galois a questioni di statistica, Rend. Acc. Naz. Lincei, (8) 35 (1963) 479–485.MATHMathSciNetGoogle Scholar
  20. [20]
    G. Tallini, Problemi e risultati sulle geometrie di Galois, Relaz. N. 30, Ist. Mat. Univ. Napoli, 1973.Google Scholar
  21. [21]
    G. Tallini, Graphic characterization of algebraic varieties in a Galois space, Atti Conv. Teorie Combinatorie (Rome, sept. 1973), Acc. Naz. Lincei, 1976, 1–7.Google Scholar
  22. [22]
    G. Tallini, Codici e geometrie combinatorie, Quaderno seminario Geom. Comb. n. 23, Ist. Mat. G. Castelnuovo Univ. Roma, marzo 1980.Google Scholar
  23. [23]
    G. Tallini, k-insiemi e blocking sets in PG(r,q) e in AG(r,q), Quaderno n. 1 Sem. Geom. Comb. Ist. Mat. Applicata, Fac. Ingegneria Univ. L’Aquila (1982), 1–36.Google Scholar
  24. [24]
    G. Tallini, Blocking sets nei sistemi di Steiner e d-blocking sets in PG(r,q) ed AG(r,q), Quaderno n. 3 Sem. Geom. Comb. Ist. Mat. Applicata, Fac. Ingegneria Univ. L’Aquila (1983), 1–32.Google Scholar
  25. [25]
    G. Tallini, Teoria dei k-insiemi in uno spazio di Galois. Teoria dei codici correttori, Quaderno n. 68 Sen. Geom. Comb. maggio 1985, Dip. Mat. Univ. Roma “La Sapienza” (1985), 1–141.Google Scholar
  26. [26]
    G. Tallini, Spazi parziali di rette e codici correttori, Rivista di Mat. pura e appl. Univ. di Udine (1987), 43–69.Google Scholar
  27. [27]
    G. Tallini, Linear codes associated with geometric structures, Results in Math. Birkhäuser Verlag, Basel (1987), 411–422.Google Scholar
  28. [28]
    G. Tallini, On blocking sets in finite projective and affine spaces, Annals of Discrete Math. 37 (1988), 433–450.CrossRefMathSciNetGoogle Scholar
  29. [29]
    M. Tallini Scafati, Calotte di tipo (m,n) in uno spazio di Galois Sr Rend. Acc. Naz. Lincei (8) 53 (1972), 71–81.Google Scholar
  30. [30]
    M. Tallini Scafati, Sui k-insiemi di uno spazio di Galois Sr,q a due soli caratteri nella dimensione d, Rend. Acc. Naz. Lincei (8) 60 (1976), 782–787.MATHGoogle Scholar

Copyright information

© Springer-Verlag Wien 1990

Authors and Affiliations

  • G. Tallini
    • 1
  1. 1.Università La SapienzaRomaItaly

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