Paper Info
Title
On codewords in the dual code of classical generalised quadrangles and classical polar spaces
Abstract
In [J.L. Kim, K. Mellinger, L. Storme, Small weight codewords in LDPC codes defined by (dual) classical generalised quadrangles, Des. Codes Cryptogr. 42 (1) (2007) 73-92], the codewords of small weight in the dual code of the code of points and lines of Q(4,q) are characterised. Inspired by this result, using geometrical arguments, we characterise the codewords of small weight in the dual code of the code of points and generators of Q^+(5,q) and H(5,q^2), and we present lower bounds on the weight of the codewords in the dual of the code of points and k-spaces of the classical polar spaces. Furthermore, we investigate the codewords with the largest weights in these codes, where for q even and k sufficiently small, we determine the maximum weight and characterise the codewords of maximum weight. Moreover, we show that there exists an interval such that for every even number w in this interval, there is a codeword in the dual code of Q^+(5,q), q even, with weight w and we show that there is an empty interval in the weight distribution of the dual of the code of Q(4,q), q even. To prove this, we show that a blocking set of Q(4,q), q even, of size q^2+1+r, where 0
Year
DOI
Venue
2010
10.1016/j.disc.2009.06.010
Discrete Mathematics
Keywords
Field
DocType
ovoid,linear code,sets of even type,generalised quadrangle,blocking set,polar space,generalized quadrangle,weight distribution,ldpc code,lower bound
Discrete mathematics,Blocking set,Combinatorics,Upper and lower bounds,Low-density parity-check code,Code word,Linear code,Polar space,Weight distribution,Mathematics,Dual code
Journal
Volume
Issue
ISSN
310
22
Discrete Mathematics
Citations 
PageRank 
References 
3
0.50
13
Authors
3
Name
Order
Citations
PageRank
Valentina Pepe1204.59
Leo Storme219738.07
van de voorde3357.85