Absorbing sets of codes from finite geometries

Allison Beemer, Kathryn Haymaker, Christine A. Kelley

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)1115-1131
Number of pages17
JournalCryptography and Communications
Volume11
Issue number5
DOIs
StatePublished - Sep 15 2019

Fingerprint

Absorbing Set
Finite Geometry
Geometry
Low-density Parity-check (LDPC) Codes
Girth
Graph in graph theory

Keywords

  • Absorbing sets
  • Finite geometry LDPC codes
  • Tree bounds

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Computational Theory and Mathematics
  • Applied Mathematics

Cite this

Absorbing sets of codes from finite geometries. / Beemer, Allison; Haymaker, Kathryn; Kelley, Christine A.

In: Cryptography and Communications, Vol. 11, No. 5, 15.09.2019, p. 1115-1131.

Research output: Contribution to journalArticle

Beemer, Allison ; Haymaker, Kathryn ; Kelley, Christine A. / Absorbing sets of codes from finite geometries. In: Cryptography and Communications. 2019 ; Vol. 11, No. 5. pp. 1115-1131.
@article{93d67d94d6234472a3a8ed0c89838f6c,
title = "Absorbing sets of codes from finite geometries",
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.",
keywords = "Absorbing sets, Finite geometry LDPC codes, Tree bounds",
author = "Allison Beemer and Kathryn Haymaker and Kelley, {Christine A.}",
year = "2019",
month = "9",
day = "15",
doi = "10.1007/s12095-019-0353-6",
language = "English (US)",
volume = "11",
pages = "1115--1131",
journal = "Cryptography and Communications",
issn = "1936-2447",
publisher = "Springer Publishing Company",
number = "5",

}

TY - JOUR

T1 - Absorbing sets of codes from finite geometries

AU - Beemer, Allison

AU - Haymaker, Kathryn

AU - Kelley, Christine A.

PY - 2019/9/15

Y1 - 2019/9/15

N2 - 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.

AB - 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.

KW - Absorbing sets

KW - Finite geometry LDPC codes

KW - Tree bounds

UR - http://www.scopus.com/inward/record.url?scp=85070463175&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85070463175&partnerID=8YFLogxK

U2 - 10.1007/s12095-019-0353-6

DO - 10.1007/s12095-019-0353-6

M3 - Article

AN - SCOPUS:85070463175

VL - 11

SP - 1115

EP - 1131

JO - Cryptography and Communications

JF - Cryptography and Communications

SN - 1936-2447

IS - 5

ER -