Афинни блокиращи множества
DOI :
https://doi.org/10.55630/mem.2024.53.009-017Ключови думи :
крайни афинни геометрии, крайни проективни геометрии, арки, блокиращи множества, линейни кодове, граница на БруенАбстракт
В статията е направен обзор на известните резултати върху задачата за намиране на минималната мощност на блокиращо множество в AG(n, q).
Литература (библиография)
N. Alon. Combinatorial Nullstellensatz. Combin. Probab. and Computation, 8, no. 1–2 (1999), 7–29.
S. Ball. On intersection sets in Desarguesian affine spaces. European J. Comb., 21 (2000), 441–446.
S. Ball. On sets of vectors of a finite vector space in which every subset of basis size is a basis. J. Eur. Math. Soc., 14 (2012) 733–748.
S. Ball, J. De Beule. On sets of vectors of a finite vector space in which every subset of basis size is a basis II. Des. Codes Cryptogr., 65 (2012) 5–14.
S. Ball, A. Blokhuis. A bound for the maximum weight of a linear code. SIAM J. Discrete Math., 27 (2013) 575–583.
S. Ball. A p-adic condition on the weight of a codeword of a linear code. Des. Codes Cryptogr., 72 (2014) 177–183.
A. Blokhuis. On multiple nuclei and a conjecture of Lunelli and Sce. Bull. Belg. Math. Soc. Simon Stevin, 3 (1994), 349–353.
A. E. Brouwer, A. Schrijver. The blocking number of an affine space. J. Combin. Th. Ser. A, 24 (1978), 251–253.
A. A. Bruen. Polynomial multiplicities over finite fields and intersection sets. J. Comb. Th. Ser. A, 60 (1992), 19–33.
M. Grassl. Code Tables: Bounds on the parameters of various types of codes, http://codetables.markus-grassl.de.
R. Jamison. Covering finite fields with cosets of subspaces. J. Comb. Th. Ser. A/ 22 (1977), 253–256.
I. Landjev. Linear codes over finite fields and finite projective geometries. Discrete Mathematics, 213 (2000), 211–214.
I. Landjev. The geometric approach to linear codes, in: Finite Geometries (eds A. Blokhuis, J. Hirschfeld, D. Jungnickel, J. Thas), Ser. Developments in Mathematics, 2001, 247–257.
I. Landjev, A. Rousseva. On the sharpness of Bruen’s bound for intersection sets in Desarguesian affine spaces. Designs, Codes and Cryptography, 72 (2014), 551–558.
I. Landjev, A. Rousseva. A General Construction for Affine Blocking Sets, Results in Mathematics 75 (2020), #142.
I. Landjev, L. Storme. Linear codes and Galois geometries, chapter 8 in: “Current research topics in Galois geometries” (eds. L. Storme and J. De Beule), NOVA Publishers, 2012, 187–214.
C. Zanella. Intersection sets in AG(n, q) and a characterization of the hyperbolic quadric in PG(3, q). Discrete Math. 255 (2002), 381–386.
