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• W2026448191 startingPage "405" @default.
• W2026448191 abstract "We look at low density parity check codes over a finite field $mathbb K$ associated with finite geometries $T$2*$(mathcal K)$, where $mathcal K$ is any subset of PG$(2,q)$, with $q=p$h, $p$≠char$mathbb K$. This includes the geometry $LU(3,q)$D, the generalized quadrangle $T$2*$(mathcal K)$ with $mathcal K$ a hyperoval, the affine space AG$(3,q)$ and several partial and semi-partial geometries. In some cases the dimension and/or the code words of minimum weight are known. We prove an expression for the dimension and the minimum weight of the code. We classify the code words of minimum weight. We show that the code is generated completely by its words of minimum weight. We end with some practical considerations on the choice of $mathcal K$." @default.
• W2026448191 created "2016-06-24" @default.
• W2026448191 creator A5083955784 @default.
• W2026448191 date "2010-01-01" @default.
• W2026448191 modified "2023-09-26" @default.
• W2026448191 title "LDPC codes associated with linear representations of geometries" @default.
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• W2026448191 doi "https://doi.org/10.3934/amc.2010.4.405" @default.
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