Paper Info
Title
On the code generated by the incidence matrix of points and hyperplanes in PG(n,q) and its dual
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).
Year
DOI
Venue
2008
10.1007/s10623-008-9203-9
Finite Fields and Their Applications
Keywords
DocType
Volume
small weight,dual code,incidence matrix,geom dedicata,divisibility condition,desarguesian projective space,possible codewords,minimum weight,p h,projective spaces · linear codes · blocking sets · small weight codewords,p-ary linear code,projective space,code generation,linear code,lower bound
Journal
48
Issue
ISSN
Citations 
3
Des. Codes Cryptogr. 48 (2008), no. 3, 231--245
10
PageRank 
References 
Authors
1.10
7
3
Name
Order
Citations
PageRank
Michel Lavrauw16917.63
Leo Storme219738.07
van de voorde3357.85