scholarly journals Rédei Blocking Sets in Finite Desarguesian Planes

2002 ◽  
Vol 98 (2) ◽  
pp. 343-356
Author(s):  
B.F. Sherman
Keyword(s):  
Blocking Sets ◽  
Desarguesian Planes ◽  
Rédei Blocking Sets

Multiple blocking sets and multisets in Desarguesian planes

2010 ◽  
Vol 56 (2-3) ◽  
pp. 177-181 ◽  
Author(s):  
Angela Aguglia ◽  
Gábor Korchmáros
Keyword(s):  
Blocking Sets ◽  
Desarguesian Planes

scholarly journals Codes from Cubic Curves and their Extensions

10.37236/766 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
T. L. Alderson ◽  
A. A. Bruen
Keyword(s):  
Linear Code ◽  
Linear Codes ◽  
Mds Codes ◽  
Blocking Sets ◽  
Linear Extensions ◽  
Cubic Curves ◽  
Cubic Curve ◽  
Rédei Blocking Sets

We study the linear codes and their extensions associated with sets of points in the plane corresponding to cubic curves. Instead of merely studying linear extensions, all possible extensions of the code are studied. In this way several new results are obtained and some existing results are strengthened. This type of analysis was carried out by Alderson, Bruen, and Silverman [J. Combin. Theory Ser. A, 114(6), 2007] for the case of MDS codes and by the present authors [Des. Codes Cryptogr., 47(1-3), 2008] for a broader range of codes. The methods cast some light on the question as to when a linear code can be extended to a nonlinear code. For example, for $p$ prime, it is shown that a linear $[n,3,n-3]_p$ code corresponding to a non-singular cubic curve comprising $n> p+4$ points admits only extensions that are equivalent to linear codes. The methods involve the theory of Rédei blocking sets and the use of the Bruen-Silverman model of linear codes.

scholarly journals Full Characterization of Minimal Linear Codes as Cutting Blocking Sets

2021 ◽  
pp. 1-1
Author(s):  
Chunming Tang ◽  
Yan Qiu ◽  
Qunying Liao ◽  
Zhengchun Zhou
Keyword(s):  
Linear Codes ◽  
Blocking Sets ◽  
Full Characterization

Blocking sets in 3-designs

1989 ◽  
Vol 35 (1-2) ◽  
pp. 75-86 ◽  
Author(s):  
Mario Gionfriddo ◽  
Biagio Micale
Keyword(s):  
Blocking Sets

scholarly journals The size of m-irreducible blocking sets and of the sets of class [0,n1,…,nl]

2008 ◽  
Vol 308 (2-3) ◽  
pp. 180-183
Author(s):  
S. Rajola ◽  
M. Scafati Tallini
Keyword(s):  
Blocking Sets

scholarly journals The Lower Bounds of Eight and Fourth Blocking Sets and Existence of Minimal Blocking Sets

2007 ◽  
Vol 19 (3) ◽  
pp. 99-111
Author(s):  
L.Yasin Nada Yassen Kasm Yahya ◽  
Abdul Khalik
Keyword(s):  
Lower Bounds ◽  
Blocking Sets ◽  
Minimal Blocking

scholarly journals Blocking sets for cycles and paths designs

2020 ◽  
Vol 14 (1) ◽  
pp. 183-197
Author(s):  
Paola Bonacini ◽  
Lucia Marino
Keyword(s):  
Blocking Set ◽  
Blocking Sets

In this paper, we study blocking sets for C4, P3 and P5-designs. In the case of C4-designs and P3-designs we determine the cases in which the blocking sets have the largest possible range of cardinalities. These designs are called largely blocked. Moreover, a blocking set T for a G-design is called perfect if in any block the number of edges between elements of T and elements in the complement is equal to a constant. In this paper, we consider perfect blocking sets for C4-designs and P5-designs.

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