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Locally repairable codes (LRCs) with locality *r* and availability *t* are a class of codes which can recover data from erasures by accessing other *t* disjoint repair groups, that every group contain at most *r* other code symbols. This letter will investigate constructions of LRCs derived from cyclic codes and generalized quadrangle. On the one hand, two classes of cyclic LRC with given locality *m*-1 and availability *em* are proposed via trace function. Our LRCs have the same locality, availability, minimum distance and code rate, but have short length and low dimension. On the other hand, an LRC with $(2,(p+1)lfloorrac{s}{2}
floor)$ is presented based on sets of points in *PG*(*k*, *q*) which form generalized quadrangles with order (*s*, *p*). For *k*=3, 4, 5, LRCs with *r*=2 and different *t* are determined.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E103-A No.7 pp.947-950

- Publication Date
- 2020/07/01

- Publicized

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.2019EAL2170

- Type of Manuscript
- LETTER

- Category
- Coding Theory

Qiang FU

Air Force Engineering University

Ruihu LI

Air Force Engineering University

Luobin GUO

Air Force Engineering University

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.

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Qiang FU, Ruihu LI, Luobin GUO, "Locally Repairable Codes from Cyclic Codes and Generalized Quadrangles" in IEICE TRANSACTIONS on Fundamentals,
vol. E103-A, no. 7, pp. 947-950, July 2020, doi: 10.1587/transfun.2019EAL2170.

Abstract: Locally repairable codes (LRCs) with locality *r* and availability *t* are a class of codes which can recover data from erasures by accessing other *t* disjoint repair groups, that every group contain at most *r* other code symbols. This letter will investigate constructions of LRCs derived from cyclic codes and generalized quadrangle. On the one hand, two classes of cyclic LRC with given locality *m*-1 and availability *em* are proposed via trace function. Our LRCs have the same locality, availability, minimum distance and code rate, but have short length and low dimension. On the other hand, an LRC with $(2,(p+1)lfloorrac{s}{2}
floor)$ is presented based on sets of points in *PG*(*k*, *q*) which form generalized quadrangles with order (*s*, *p*). For *k*=3, 4, 5, LRCs with *r*=2 and different *t* are determined.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2019EAL2170/_p

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@ARTICLE{e103-a_7_947,

author={Qiang FU, Ruihu LI, Luobin GUO, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Locally Repairable Codes from Cyclic Codes and Generalized Quadrangles},

year={2020},

volume={E103-A},

number={7},

pages={947-950},

abstract={Locally repairable codes (LRCs) with locality *r* and availability *t* are a class of codes which can recover data from erasures by accessing other *t* disjoint repair groups, that every group contain at most *r* other code symbols. This letter will investigate constructions of LRCs derived from cyclic codes and generalized quadrangle. On the one hand, two classes of cyclic LRC with given locality *m*-1 and availability *em* are proposed via trace function. Our LRCs have the same locality, availability, minimum distance and code rate, but have short length and low dimension. On the other hand, an LRC with $(2,(p+1)lfloorrac{s}{2}
floor)$ is presented based on sets of points in *PG*(*k*, *q*) which form generalized quadrangles with order (*s*, *p*). For *k*=3, 4, 5, LRCs with *r*=2 and different *t* are determined.},

keywords={},

doi={10.1587/transfun.2019EAL2170},

ISSN={1745-1337},

month={July},}

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TY - JOUR

TI - Locally Repairable Codes from Cyclic Codes and Generalized Quadrangles

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 947

EP - 950

AU - Qiang FU

AU - Ruihu LI

AU - Luobin GUO

PY - 2020

DO - 10.1587/transfun.2019EAL2170

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E103-A

IS - 7

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - July 2020

AB - Locally repairable codes (LRCs) with locality *r* and availability *t* are a class of codes which can recover data from erasures by accessing other *t* disjoint repair groups, that every group contain at most *r* other code symbols. This letter will investigate constructions of LRCs derived from cyclic codes and generalized quadrangle. On the one hand, two classes of cyclic LRC with given locality *m*-1 and availability *em* are proposed via trace function. Our LRCs have the same locality, availability, minimum distance and code rate, but have short length and low dimension. On the other hand, an LRC with $(2,(p+1)lfloorrac{s}{2}
floor)$ is presented based on sets of points in *PG*(*k*, *q*) which form generalized quadrangles with order (*s*, *p*). For *k*=3, 4, 5, LRCs with *r*=2 and different *t* are determined.

ER -