Small weight codewords in the LDPC codes arising from linear representations of geometries
✍ Scribed by V. Pepe; L. Storme; G. Van de Voorde
- Publisher
- John Wiley and Sons
- Year
- 2009
- Tongue
- English
- Weight
- 242 KB
- Volume
- 17
- Category
- Article
- ISSN
- 1063-8539
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✦ Synopsis
Abstract
In 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, hence q even, 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