The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Untuk [n, k, d] (r, δ)-kod boleh dibaiki secara tempatan ((r, δ)-LRCs), jarak minimumnya d memenuhi terikat seperti Singleton. Pembinaan optimum (r, δ)-LRC, mencapai ikatan seperti Singleton ini, merupakan masalah penyelidikan penting dalam beberapa tahun kebelakangan ini untuk aplikasi mereka dalam sistem storan teragih. Dalam surat ini, kami menggunakan kod Reed-Solomon untuk membina dua kelas optimum (r, δ)-LRC. LRC optimum diberikan oleh penilaian berbilang polinomial darjah paling banyak r - 1 pada beberapa titik dalam Fq. Kelas pertama memberikan [(r + δ - 1)t, rt - s, δ + s] optimum (r, δ)-LRC tamat Fq dengan syarat bahawa r + δ + s - 1≤q, s≤δ, s<r, dan mana-mana yang positif t. Panjang kod tidak terhad. Kelas kedua memberikan [r + r' + d + δ - 2, r + r', d] optimum (r, δ)-LRC tamat Fq dengan syarat bahawa r - r'≥d - δ dan r + d - 1≤q + 1, yang akan menghasilkan optimum (r, δ)-LRC dengan jarak minimum yang besar.
Lin-Zhi SHEN
Civil Aviation University of China
Yu-Jie WANG
Civil Aviation University of China
The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.
Salinan
Lin-Zhi SHEN, Yu-Jie WANG, "Optimal (r, δ)-Locally Repairable Codes from Reed-Solomon Codes" in IEICE TRANSACTIONS on Fundamentals,
vol. E106-A, no. 12, pp. 1589-1592, December 2023, doi: 10.1587/transfun.2023EAL2026.
Abstract: For an [n, k, d] (r, δ)-locally repairable codes ((r, δ)-LRCs), its minimum distance d satisfies the Singleton-like bound. The construction of optimal (r, δ)-LRC, attaining this Singleton-like bound, is an important research problem in recent years for thier applications in distributed storage systems. In this letter, we use Reed-Solomon codes to construct two classes of optimal (r, δ)-LRCs. The optimal LRCs are given by the evaluations of multiple polynomials of degree at most r - 1 at some points in Fq. The first class gives the [(r + δ - 1)t, rt - s, δ + s] optimal (r, δ)-LRC over Fq provided that r + δ + s - 1≤q, s≤δ, s<r, and any positive t. The code length is unbounded. The second class gives the [r + r' + d + δ - 2, r + r', d] optimal (r, δ)-LRC over Fq provided that r - r'≥d - δ and r + d - 1≤q + 1, which will produce optimal (r, δ)-LRCs with large minimum distance.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2023EAL2026/_p
Salinan
@ARTICLE{e106-a_12_1589,
author={Lin-Zhi SHEN, Yu-Jie WANG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Optimal (r, δ)-Locally Repairable Codes from Reed-Solomon Codes},
year={2023},
volume={E106-A},
number={12},
pages={1589-1592},
abstract={For an [n, k, d] (r, δ)-locally repairable codes ((r, δ)-LRCs), its minimum distance d satisfies the Singleton-like bound. The construction of optimal (r, δ)-LRC, attaining this Singleton-like bound, is an important research problem in recent years for thier applications in distributed storage systems. In this letter, we use Reed-Solomon codes to construct two classes of optimal (r, δ)-LRCs. The optimal LRCs are given by the evaluations of multiple polynomials of degree at most r - 1 at some points in Fq. The first class gives the [(r + δ - 1)t, rt - s, δ + s] optimal (r, δ)-LRC over Fq provided that r + δ + s - 1≤q, s≤δ, s<r, and any positive t. The code length is unbounded. The second class gives the [r + r' + d + δ - 2, r + r', d] optimal (r, δ)-LRC over Fq provided that r - r'≥d - δ and r + d - 1≤q + 1, which will produce optimal (r, δ)-LRCs with large minimum distance.},
keywords={},
doi={10.1587/transfun.2023EAL2026},
ISSN={1745-1337},
month={December},}
Salinan
TY - JOUR
TI - Optimal (r, δ)-Locally Repairable Codes from Reed-Solomon Codes
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1589
EP - 1592
AU - Lin-Zhi SHEN
AU - Yu-Jie WANG
PY - 2023
DO - 10.1587/transfun.2023EAL2026
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E106-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2023
AB - For an [n, k, d] (r, δ)-locally repairable codes ((r, δ)-LRCs), its minimum distance d satisfies the Singleton-like bound. The construction of optimal (r, δ)-LRC, attaining this Singleton-like bound, is an important research problem in recent years for thier applications in distributed storage systems. In this letter, we use Reed-Solomon codes to construct two classes of optimal (r, δ)-LRCs. The optimal LRCs are given by the evaluations of multiple polynomials of degree at most r - 1 at some points in Fq. The first class gives the [(r + δ - 1)t, rt - s, δ + s] optimal (r, δ)-LRC over Fq provided that r + δ + s - 1≤q, s≤δ, s<r, and any positive t. The code length is unbounded. The second class gives the [r + r' + d + δ - 2, r + r', d] optimal (r, δ)-LRC over Fq provided that r - r'≥d - δ and r + d - 1≤q + 1, which will produce optimal (r, δ)-LRCs with large minimum distance.
ER -