Moderate-density parity-check codes from projective bundles

DOI10.1007/s10623-022-01054-yOpenAlexW3137996399WikidataQ114849735 ScholiaQ114849735MaRDI QIDQ2099159

Sam Mattheus, Jessica Bariffi, Alessandro Neri, Joachim Rosenthal

Publication date: 23 November 2022

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.09722

zbMATH Keywords

projective planeprojective bundleMDPC codesbit-flipping decoding algorithm

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Linear codes (general theory) (94B05) General block designs in finite geometry (51E05)

Uses Software

• McEliece

Cites Work

• LDPC codes associated with linear representations of geometries
• Explicit constructions of graphs without short cycles and low density codes
• Projective bundles
• Projective geometric codes
• Small weight codewords of projective geometric codes
• Small weight codewords in LDPC codes defined by (dual) classical generalized quadrangles
• On linear sets on a projective line
• The Non-Existence of Finite Projective Planes of Order 10
• Explicit Construction of Families of LDPC Codes With No<tex>$4$</tex>-Cycles
• LDPC Codes From Generalized Polygons
• Codes on finite geometries
• Small weight codewords in the LDPC codes arising from linear representations of geometries
• Design of capacity-approaching irregular low-density parity-check codes
• Low-density parity-check codes based on finite geometries: a rediscovery and new results
• A class of majority logic decodable codes (Corresp.)
• On the Number of Information Symbols in Difference-Set Cyclic Codes
• A geometric approach to a class of cyclic codes
• Ovals In a Finite Projective Plane
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