Rank Metric Codes and Their Galois Duality
Summary :
In this paper, we describe the Galois dual of rank metric codes in the ambient space FQn×m and FQmn, where Q=qe. We obtain connections between the duality of rank metric codes with respect to distinct Galois inner products. Furthermore, for 0 ≤ s < e, we introduce the concept of qsm-dual bases of FQm over FQ and obtain some conditions about the existence of qsm-self-dual basis.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E106-A No.8 pp.1067-1071
- Publication Date
- 2023/08/01
- Publicized
- 2023/02/20
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.2022EAL2090
- Type of Manuscript
- LETTER
- Category
- Coding Theory
Authors
Qing GAO
Shanghai University
Yang DING
Shanghai University,Newtouch Center for Mathematics of Shanghai University
Keyword
Latest Issue
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Qing GAO, Yang DING, "Rank Metric Codes and Their Galois Duality" in IEICE TRANSACTIONS on Fundamentals,
vol. E106-A, no. 8, pp. 1067-1071, August 2023, doi: 10.1587/transfun.2022EAL2090.
Abstract: In this paper, we describe the Galois dual of rank metric codes in the ambient space FQn×m and FQmn, where Q=qe. We obtain connections between the duality of rank metric codes with respect to distinct Galois inner products. Furthermore, for 0 ≤ s < e, we introduce the concept of qsm-dual bases of FQm over FQ and obtain some conditions about the existence of qsm-self-dual basis.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2022EAL2090/_p
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@ARTICLE{e106-a_8_1067,
author={Qing GAO, Yang DING, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Rank Metric Codes and Their Galois Duality},
year={2023},
volume={E106-A},
number={8},
pages={1067-1071},
abstract={In this paper, we describe the Galois dual of rank metric codes in the ambient space FQn×m and FQmn, where Q=qe. We obtain connections between the duality of rank metric codes with respect to distinct Galois inner products. Furthermore, for 0 ≤ s < e, we introduce the concept of qsm-dual bases of FQm over FQ and obtain some conditions about the existence of qsm-self-dual basis.},
keywords={},
doi={10.1587/transfun.2022EAL2090},
ISSN={1745-1337},
month={August},}
Copy
TY - JOUR
TI - Rank Metric Codes and Their Galois Duality
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1067
EP - 1071
AU - Qing GAO
AU - Yang DING
PY - 2023
DO - 10.1587/transfun.2022EAL2090
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E106-A
IS - 8
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - August 2023
AB - In this paper, we describe the Galois dual of rank metric codes in the ambient space FQn×m and FQmn, where Q=qe. We obtain connections between the duality of rank metric codes with respect to distinct Galois inner products. Furthermore, for 0 ≤ s < e, we introduce the concept of qsm-dual bases of FQm over FQ and obtain some conditions about the existence of qsm-self-dual basis.
ER -
English
