Abstract
We examine the presence of absorbing sets, fully absorbing sets, and elementary absorbing sets in low-density parity-check (LDPC) codes arising from certain classes of finite geometries. In particular, we prove the parameters of the smallest absorbing sets for finite geometry codes using a tree-based argument. Moreover, we obtain the parameters of the smallest absorbing sets for a special class of codes whose graphs are d-left-regular with girth g = 6 or g = 8.
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Acknowledgements
K. Haymaker would like to thank Pascal Vontobel for noting an error in Lemma 2 of [1], which was helpful in the preparation of this paper.
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Beemer, A., Haymaker, K. & Kelley, C.A. Absorbing sets of codes from finite geometries. Cryptogr. Commun. 11, 1115–1131 (2019). https://doi.org/10.1007/s12095-019-0353-6
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DOI: https://doi.org/10.1007/s12095-019-0353-6