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

2 Citations (Scopus)

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
Pages (from-to)	309-329
Number of pages	21
Journal	Designs, Codes, and Cryptography
Volume	93
Issue number	2
DOIs	https://doi.org/10.1007/s10623-023-01255-z
Publication status	Published - Feb 2025

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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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",

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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.

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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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Linear codes from arcs and quadrics

Abstract

Keywords

ASJC Scopus subject areas

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