The search functionality is under construction.

The search functionality is under construction.

One of the main problems in list decoding is to determine the tradeoff between the list decoding radius and the rate of the codes w.r.t. a given metric. In this paper, we first describe a “stronger-weaker” relationship between two distinct metrics of the same code, then we show that the list decodability of the stronger metric can be deduced from the weaker metric directly. In particular, when we focus on matrix codes, we can obtain list decodability of matrix code w.r.t. the cover metric from the Hamming metric and the rank metric. Moreover, we deduce a Johnson-like bound of the list decoding radius for cover metric codes, which improved the result of [20]. In addition, the condition for a metric that whether the list decoding radius w.r.t. this metric and the rate are bounded by the Singleton bound is presented.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E104-A No.10 pp.1430-1434

- Publication Date
- 2021/10/01

- Publicized
- 2021/03/29

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.2021EAL2015

- Type of Manuscript
- LETTER

- Category
- Coding Theory

Yang DING

Shanghai University

Yuting QIU

Shanghai University

Hongxi TONG

Shanghai 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.

Copy

Yang DING, Yuting QIU, Hongxi TONG, "On the List Decodability of Matrix Codes with Different Metrics" in IEICE TRANSACTIONS on Fundamentals,
vol. E104-A, no. 10, pp. 1430-1434, October 2021, doi: 10.1587/transfun.2021EAL2015.

Abstract: One of the main problems in list decoding is to determine the tradeoff between the list decoding radius and the rate of the codes w.r.t. a given metric. In this paper, we first describe a “stronger-weaker” relationship between two distinct metrics of the same code, then we show that the list decodability of the stronger metric can be deduced from the weaker metric directly. In particular, when we focus on matrix codes, we can obtain list decodability of matrix code w.r.t. the cover metric from the Hamming metric and the rank metric. Moreover, we deduce a Johnson-like bound of the list decoding radius for cover metric codes, which improved the result of [20]. In addition, the condition for a metric that whether the list decoding radius w.r.t. this metric and the rate are bounded by the Singleton bound is presented.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2021EAL2015/_p

Copy

@ARTICLE{e104-a_10_1430,

author={Yang DING, Yuting QIU, Hongxi TONG, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={On the List Decodability of Matrix Codes with Different Metrics},

year={2021},

volume={E104-A},

number={10},

pages={1430-1434},

abstract={One of the main problems in list decoding is to determine the tradeoff between the list decoding radius and the rate of the codes w.r.t. a given metric. In this paper, we first describe a “stronger-weaker” relationship between two distinct metrics of the same code, then we show that the list decodability of the stronger metric can be deduced from the weaker metric directly. In particular, when we focus on matrix codes, we can obtain list decodability of matrix code w.r.t. the cover metric from the Hamming metric and the rank metric. Moreover, we deduce a Johnson-like bound of the list decoding radius for cover metric codes, which improved the result of [20]. In addition, the condition for a metric that whether the list decoding radius w.r.t. this metric and the rate are bounded by the Singleton bound is presented.},

keywords={},

doi={10.1587/transfun.2021EAL2015},

ISSN={1745-1337},

month={October},}

Copy

TY - JOUR

TI - On the List Decodability of Matrix Codes with Different Metrics

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 1430

EP - 1434

AU - Yang DING

AU - Yuting QIU

AU - Hongxi TONG

PY - 2021

DO - 10.1587/transfun.2021EAL2015

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E104-A

IS - 10

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - October 2021

AB - One of the main problems in list decoding is to determine the tradeoff between the list decoding radius and the rate of the codes w.r.t. a given metric. In this paper, we first describe a “stronger-weaker” relationship between two distinct metrics of the same code, then we show that the list decodability of the stronger metric can be deduced from the weaker metric directly. In particular, when we focus on matrix codes, we can obtain list decodability of matrix code w.r.t. the cover metric from the Hamming metric and the rank metric. Moreover, we deduce a Johnson-like bound of the list decoding radius for cover metric codes, which improved the result of [20]. In addition, the condition for a metric that whether the list decoding radius w.r.t. this metric and the rate are bounded by the Singleton bound is presented.

ER -