Linearized Reed-Solomon Codes with Support-Constrained Generator Matrix

Hedongliang Liu; Hengjia Wei; Antonia Wachter-Zeh; Moshe Schwartz

doi:10.1109/ITW55543.2023.10161635

Linearized Reed-Solomon Codes with Support-Constrained Generator Matrix

Hedongliang Liu, Hengjia Wei, Antonia Wachter-Zeh, Moshe Schwartz

Associate Professorship of Coding and Cryptography

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Scopus citations

Abstract

Linearized Reed-Solomon (LRS) codes are a class of evaluation codes based on skew polynomials. They achieve the Singleton bound in the sum-rank metric, and therefore are known as maximum sum-rank distance (MSRD) codes. In this work, we give necessary and sufficient conditions on the existence of MSRD codes with support-constrained generator matrix. These conditions are identical to those for MDS codes and MRD codes. Moreover, the required field size for an [ {n,k} ]qm LRS codes with support-constrained generator matrix is q≥ ℓ + 1 and m ≥ maxl∈[ℓ]{k-1+logqk,nl}, where ℓ is the number of blocks and nl is the size of the l-th block. The special cases of the result coincide with the known results for Reed-Solomon codes and Gabidulin codes.

Original language	English
Title of host publication	2023 IEEE Information Theory Workshop, ITW 2023
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	7-12
Number of pages	6
ISBN (Electronic)	9798350301496
DOIs	https://doi.org/10.1109/ITW55543.2023.10161635
State	Published - 2023
Event	2023 IEEE Information Theory Workshop, ITW 2023 - Saint-Malo, France Duration: 23 Apr 2023 → 28 Apr 2023

Publication series

Name	2023 IEEE Information Theory Workshop, ITW 2023

Conference

Conference	2023 IEEE Information Theory Workshop, ITW 2023
Country/Territory	France
City	Saint-Malo
Period	23/04/23 → 28/04/23

Access to Document

10.1109/ITW55543.2023.10161635

Cite this

@inproceedings{019bb47c7b554de4a40a263d74557181,

title = "Linearized Reed-Solomon Codes with Support-Constrained Generator Matrix",

abstract = "Linearized Reed-Solomon (LRS) codes are a class of evaluation codes based on skew polynomials. They achieve the Singleton bound in the sum-rank metric, and therefore are known as maximum sum-rank distance (MSRD) codes. In this work, we give necessary and sufficient conditions on the existence of MSRD codes with support-constrained generator matrix. These conditions are identical to those for MDS codes and MRD codes. Moreover, the required field size for an [ {n,k} ]qm LRS codes with support-constrained generator matrix is q≥ ℓ + 1 and m ≥ maxl∈[ℓ]{k-1+logqk,nl}, where ℓ is the number of blocks and nl is the size of the l-th block. The special cases of the result coincide with the known results for Reed-Solomon codes and Gabidulin codes.",

author = "Hedongliang Liu and Hengjia Wei and Antonia Wachter-Zeh and Moshe Schwartz",

note = "Publisher Copyright: {\textcopyright} 2023 IEEE.; 2023 IEEE Information Theory Workshop, ITW 2023 ; Conference date: 23-04-2023 Through 28-04-2023",

year = "2023",

doi = "10.1109/ITW55543.2023.10161635",

language = "English",

series = "2023 IEEE Information Theory Workshop, ITW 2023",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "7--12",

booktitle = "2023 IEEE Information Theory Workshop, ITW 2023",

}

Liu, H, Wei, H, Wachter-Zeh, A & Schwartz, M 2023, Linearized Reed-Solomon Codes with Support-Constrained Generator Matrix. in 2023 IEEE Information Theory Workshop, ITW 2023. 2023 IEEE Information Theory Workshop, ITW 2023, Institute of Electrical and Electronics Engineers Inc., pp. 7-12, 2023 IEEE Information Theory Workshop, ITW 2023, Saint-Malo, France, 23/04/23. https://doi.org/10.1109/ITW55543.2023.10161635

Linearized Reed-Solomon Codes with Support-Constrained Generator Matrix. / Liu, Hedongliang; Wei, Hengjia; Wachter-Zeh, Antonia et al.
2023 IEEE Information Theory Workshop, ITW 2023. Institute of Electrical and Electronics Engineers Inc., 2023. p. 7-12 (2023 IEEE Information Theory Workshop, ITW 2023).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Linearized Reed-Solomon Codes with Support-Constrained Generator Matrix

AU - Liu, Hedongliang

AU - Wei, Hengjia

AU - Wachter-Zeh, Antonia

AU - Schwartz, Moshe

PY - 2023

Y1 - 2023

N2 - Linearized Reed-Solomon (LRS) codes are a class of evaluation codes based on skew polynomials. They achieve the Singleton bound in the sum-rank metric, and therefore are known as maximum sum-rank distance (MSRD) codes. In this work, we give necessary and sufficient conditions on the existence of MSRD codes with support-constrained generator matrix. These conditions are identical to those for MDS codes and MRD codes. Moreover, the required field size for an [ {n,k} ]qm LRS codes with support-constrained generator matrix is q≥ ℓ + 1 and m ≥ maxl∈[ℓ]{k-1+logqk,nl}, where ℓ is the number of blocks and nl is the size of the l-th block. The special cases of the result coincide with the known results for Reed-Solomon codes and Gabidulin codes.

AB - Linearized Reed-Solomon (LRS) codes are a class of evaluation codes based on skew polynomials. They achieve the Singleton bound in the sum-rank metric, and therefore are known as maximum sum-rank distance (MSRD) codes. In this work, we give necessary and sufficient conditions on the existence of MSRD codes with support-constrained generator matrix. These conditions are identical to those for MDS codes and MRD codes. Moreover, the required field size for an [ {n,k} ]qm LRS codes with support-constrained generator matrix is q≥ ℓ + 1 and m ≥ maxl∈[ℓ]{k-1+logqk,nl}, where ℓ is the number of blocks and nl is the size of the l-th block. The special cases of the result coincide with the known results for Reed-Solomon codes and Gabidulin codes.

UR - http://www.scopus.com/inward/record.url?scp=85165024221&partnerID=8YFLogxK

U2 - 10.1109/ITW55543.2023.10161635

DO - 10.1109/ITW55543.2023.10161635

M3 - Conference contribution

AN - SCOPUS:85165024221

T3 - 2023 IEEE Information Theory Workshop, ITW 2023

SP - 7

EP - 12

BT - 2023 IEEE Information Theory Workshop, ITW 2023

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2023 IEEE Information Theory Workshop, ITW 2023

Y2 - 23 April 2023 through 28 April 2023

ER -

Linearized Reed-Solomon Codes with Support-Constrained Generator Matrix

Abstract

Publication series

Conference

Access to Document

Other files and links

Fingerprint

Cite this