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Absorbing sets of codes from finite geometries

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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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Authors and Affiliations

  1. Arizona State University, P.O. Box 875706, Tempe, AZ, 85287, USA

    Allison Beemer

  2. Villanova University, 800 E. Lancaster Ave, Villanova, PA, 19085, USA

    Kathryn Haymaker

  3. University of Nebraska-Lincoln, 1400 R Street, Lincoln, NE, 68588, USA

    Christine A. Kelley

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  1. Allison Beemer
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  2. Kathryn Haymaker
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  3. Christine A. Kelley
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Correspondence to Kathryn Haymaker.

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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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