Point-line incidence on Grassmannians and majority logic decoding of Grassmann codes

Peter Beelen; Prasant Singh

doi:10.1016/j.ffa.2021.101843

Point-line incidence on Grassmannians and majority logic decoding of Grassmann codes

Peter Beelen, Prasant Singh^*

^*Corresponding author for this work

University of Tromsø

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Abstract

In this article, we consider the decoding problem of Grassmann codes using majority logic. We show that for two points of the Grassmannian, there exists a canonical geodesic between these points once a complete flag is fixed. These geodesics are used to construct a large set of parity checks orthogonal on a coordinate of the code, resulting in a majority decoding algorithm.

Original language	English
Article number	101843
Journal	Finite Fields and Their Applications
Volume	73
Number of pages	24
ISSN	1071-5797
DOIs	https://doi.org/10.1016/j.ffa.2021.101843
Publication status	Published - Aug 2021

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Publisher Copyright:
© 2021 Elsevier Inc.

Keywords

Grassmann codes
Grassmann varieties
Majority logic
Point-line incidence
Schubert varieties

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10.1016/j.ffa.2021.101843

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AB - In this article, we consider the decoding problem of Grassmann codes using majority logic. We show that for two points of the Grassmannian, there exists a canonical geodesic between these points once a complete flag is fixed. These geodesics are used to construct a large set of parity checks orthogonal on a coordinate of the code, resulting in a majority decoding algorithm.

KW - Grassmann codes

KW - Grassmann varieties

KW - Majority logic

KW - Point-line incidence

KW - Schubert varieties

U2 - 10.1016/j.ffa.2021.101843

DO - 10.1016/j.ffa.2021.101843

M3 - Journal article

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JO - Finite Fields and Their Applications

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Point-line incidence on Grassmannians and majority logic decoding of Grassmann codes

Abstract

Bibliographical note

Keywords

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