Linear codes from arcs and quadrics

Kanat Abdukhalikov; Duy Ho

doi:10.1007/s10623-023-01255-z

Linear codes from arcs and quadrics

Kanat Abdukhalikov, Duy Ho

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

Using characterizations of ovals, KM-arcs and elliptic quadrics recently described in polar coordinates, we construct some families of LCD, self-orthogonal, three-weight and four-weight linear codes. We also demonstrate some applications to quantum codes.

Original language	English
Journal	Designs, Codes, and Cryptography
DOIs	https://doi.org/10.1007/s10623-023-01255-z
Publication status	Accepted/In press - 2023

Keywords

Hyperovals
KM-arcs
LCD codes
Linear codes
Linear codes with few weights
Ovoids
Quantum codes
Self-orthogonal codes

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science Applications
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1007/s10623-023-01255-z

Cite this

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title = "Linear codes from arcs and quadrics",

abstract = "Using characterizations of ovals, KM-arcs and elliptic quadrics recently described in polar coordinates, we construct some families of LCD, self-orthogonal, three-weight and four-weight linear codes. We also demonstrate some applications to quantum codes.",

keywords = "Hyperovals, KM-arcs, LCD codes, Linear codes, Linear codes with few weights, Ovoids, Quantum codes, Self-orthogonal codes",

author = "Kanat Abdukhalikov and Duy Ho",

note = "Funding Information: This work was supported by UAEU grant G00003490. Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",

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doi = "10.1007/s10623-023-01255-z",

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AU - Abdukhalikov, Kanat

AU - Ho, Duy

N1 - Funding Information: This work was supported by UAEU grant G00003490. Publisher Copyright: © 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2023

Y1 - 2023

N2 - Using characterizations of ovals, KM-arcs and elliptic quadrics recently described in polar coordinates, we construct some families of LCD, self-orthogonal, three-weight and four-weight linear codes. We also demonstrate some applications to quantum codes.

AB - Using characterizations of ovals, KM-arcs and elliptic quadrics recently described in polar coordinates, we construct some families of LCD, self-orthogonal, three-weight and four-weight linear codes. We also demonstrate some applications to quantum codes.

KW - Hyperovals

KW - KM-arcs

KW - LCD codes

KW - Linear codes

KW - Linear codes with few weights

KW - Ovoids

KW - Quantum codes

KW - Self-orthogonal codes

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JF - Designs, Codes, and Cryptography

ER -

Linear codes from arcs and quadrics

Abstract

Keywords

ASJC Scopus subject areas

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