On the Construction of Quantum and LCD Codes from Cyclic Codes over the Finite Commutative Rings

Shakir Ali; Amal S. Alali; Mohammad Jeelani; Muhammet Kurulay; Elif Segah Öztas; Pushpendra Sharma

doi:10.3390/axioms12040367

On the Construction of Quantum and LCD Codes from Cyclic Codes over the Finite Commutative Rings

Shakir Ali^*
, Amal S. Alali
, Mohammad Jeelani
, Muhammet Kurulay
, Elif Segah Öztas
, Pushpendra Sharma

^*Corresponding author for this work

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

10 Citations (Scopus)

Abstract

Let (Formula presented.) be a field of order q, where q is a power of an odd prime p, and (Formula presented.) and (Formula presented.) are two non-zero elements of (Formula presented.). The primary goal of this article is to study the structural properties of cyclic codes over a finite ring (Formula presented.). We decompose the ring R by using orthogonal idempotents (Formula presented.), and (Formula presented.) as (Formula presented.), and to construct quantum-error-correcting (QEC) codes over R. As an application, we construct some optimal LCD codes.

Original language	English
Article number	367
Journal	Axioms
Volume	12
Issue number	4
DOIs	https://doi.org/10.3390/axioms12040367
Publication status	Published - Apr 2023
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2023 by the authors.

Keywords

Gray map
LCD code
cyclic code
quantum code

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10.3390/axioms12040367

Cite this

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title = "On the Construction of Quantum and LCD Codes from Cyclic Codes over the Finite Commutative Rings",

abstract = "Let (Formula presented.) be a field of order q, where q is a power of an odd prime p, and (Formula presented.) and (Formula presented.) are two non-zero elements of (Formula presented.). The primary goal of this article is to study the structural properties of cyclic codes over a finite ring (Formula presented.). We decompose the ring R by using orthogonal idempotents (Formula presented.), and (Formula presented.) as (Formula presented.), and to construct quantum-error-correcting (QEC) codes over R. As an application, we construct some optimal LCD codes.",

keywords = "Gray map, LCD code, cyclic code, quantum code",

author = "Shakir Ali and Alali, \{Amal S.\} and Mohammad Jeelani and Muhammet Kurulay and {\"O}ztas, \{Elif Segah\} and Pushpendra Sharma",

note = "Publisher Copyright: {\textcopyright} 2023 by the authors.",

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doi = "10.3390/axioms12040367",

language = "English",

volume = "12",

journal = "Axioms",

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T1 - On the Construction of Quantum and LCD Codes from Cyclic Codes over the Finite Commutative Rings

AU - Ali, Shakir

AU - Alali, Amal S.

AU - Jeelani, Mohammad

AU - Kurulay, Muhammet

AU - Öztas, Elif Segah

AU - Sharma, Pushpendra

PY - 2023/4

Y1 - 2023/4

N2 - Let (Formula presented.) be a field of order q, where q is a power of an odd prime p, and (Formula presented.) and (Formula presented.) are two non-zero elements of (Formula presented.). The primary goal of this article is to study the structural properties of cyclic codes over a finite ring (Formula presented.). We decompose the ring R by using orthogonal idempotents (Formula presented.), and (Formula presented.) as (Formula presented.), and to construct quantum-error-correcting (QEC) codes over R. As an application, we construct some optimal LCD codes.

AB - Let (Formula presented.) be a field of order q, where q is a power of an odd prime p, and (Formula presented.) and (Formula presented.) are two non-zero elements of (Formula presented.). The primary goal of this article is to study the structural properties of cyclic codes over a finite ring (Formula presented.). We decompose the ring R by using orthogonal idempotents (Formula presented.), and (Formula presented.) as (Formula presented.), and to construct quantum-error-correcting (QEC) codes over R. As an application, we construct some optimal LCD codes.

KW - Gray map

KW - LCD code

KW - cyclic code

KW - quantum code

UR - https://www.scopus.com/pages/publications/85153583567

U2 - 10.3390/axioms12040367

DO - 10.3390/axioms12040367

M3 - Article

AN - SCOPUS:85153583567

SN - 2075-1680

VL - 12

JO - Axioms

JF - Axioms

IS - 4

M1 - 367

ER -

On the Construction of Quantum and LCD Codes from Cyclic Codes over the Finite Commutative Rings

Abstract

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Keywords

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