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Designs, Codes and Cryptography

Erschienen in:

13.10.2023

New quantum codes from self-dual codes over \(\mathbb {F}_4\)

verfasst von: Reza Dastbasteh, Petr Lisoněk

Erschienen in: Designs, Codes and Cryptography | Ausgabe 3/2024

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Abstract

We present new constructions of binary quantum codes from quaternary linear Hermitian self-dual codes. Our main ingredients for these constructions are nearly self-orthogonal cyclic or duadic codes over \(\mathbb {F}_4\). An infinite family of 0-dimensional binary quantum codes is provided. We give minimum distance lower bounds for our quantum codes in terms of the minimum distance of their ingredient linear codes. We also present new results on the minimum distance of linear cyclic codes using their fixed subcodes. Finally, we list many new record-breaking quantum codes obtained from our constructions.

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Titel: New quantum codes from self-dual codes over
verfasst von: Reza Dastbasteh
Petr Lisoněk
Publikationsdatum: 13.10.2023
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 3/2024
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-023-01306-5

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New quantum codes from self-dual codes over \(\mathbb {F}_4\)

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