Small weight codewords in the LDPC codes arising from linear representations of geometries

V. Pepe, L. Storme, G. Van de Voorde
<span title="">2009</span> <i title="Wiley"> <a target="_blank" rel="noopener" href="" style="color: black;">Journal of combinatorial designs (Print)</a> </i> &nbsp;
In this paper, 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 (Θ) and T * 2 (Θ) D with Θ a hyperoval, hence q even, and characterize codewords of small weight. When investigating the small weight codewords of T * 2 (Θ) D , we deal
more &raquo; ... th the case of Θ a regular hyperoval, i.e. 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.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.1002/jcd.20179</a> <a target="_blank" rel="external noopener" href="">fatcat:h7bc3r2p7ben7fgz4qu7sj7rwq</a> </span>
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