Abstract
AbstractIn this article, we investigate the minimum distance and small weight codewords of the LDPC codes of linear representations, using only geometrical methods. First, we present a new lower bound on the minimum distance and we present a number of cases in which this lower bound is sharp. Then we take a closer look at the cases$T_2^*(\Theta)$and$T_2^*(\Theta)^D$with$\Theta$a hyperoval, henceqeven, and characterize codewords of small weight. When investigating the small weight codewords of$T_2^*(\Theta)^D$, we deal with the case of$\Theta$a regular hyperoval, that is, a conic and its nucleus, separately, since in this case, we have a larger upper bound on the weight for which the results are valid. © 2008 Wiley Periodicals, Inc. J Combin Designs 17: 1–24, 2009
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