On the code generated by the incidence matrix of points and hyperplanes in PG(n,q) and its dual

Authors:
Michel Lavrauw;Leo Storme;Geertrui Voorde
Affiliations:
Department of Pure Mathematics and Computer Algebra, Ghent University, Ghent, Belgium 9000;Department of Pure Mathematics and Computer Algebra, Ghent University, Ghent, Belgium 9000;Department of Pure Mathematics and Computer Algebra, Ghent University, Ghent, Belgium 9000
Venue:
Designs, Codes and Cryptography
Year:
2008

Citing 5
Cited 3

Designs and their codes

Designs and their codes
Projective geometric codes

Journal of Combinatorial Theory Series A
Small weight codewords in the codes arising from Desarguesian projective planes

Designs, Codes and Cryptography
On small blocking sets and their linearity

Journal of Combinatorial Theory Series A
Blocking Sets in Desarguesian Affine and Projective Planes

Finite Fields and Their Applications

Note: An empty interval in the spectrum of small weight codewords in the code from points and k-spaces of PG(n,q)

Journal of Combinatorial Theory Series A
A study of (xvt,xvt-1)-minihypers in PG(t,q)

Journal of Combinatorial Theory Series A
On the code generated by the incidence matrix of points and k-spaces in PG(n,q) and its dual

Finite Fields and Their Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we study the p-ary linear code C(PG(n,q)), q = p h , p prime, h 驴 1, generated by the incidence matrix of points and hyperplanes of a Desarguesian projective space PG(n,q), and its dual code. We link the codewords of small weight of this code to blocking sets with respect to lines in PG(n,q) and we exclude all possible codewords arising from small linear blocking sets. We also look at the dual code of C(PG(n,q)) and we prove that finding the minimum weight of the dual code can be reduced to finding the minimum weight of the dual code of points and lines in PG(2,q). We present an improved upper bound on this minimum weight and we show that we can drop the divisibility condition on the weight of the codewords in Sachar's lower bound (Geom Dedicata 8:407---415, 1979).