IEICE TRANSACTIONS on Fundamentals
New Constructions of Sidon Spaces and Cyclic Subspace Codes
Summary :
Sidon space is an important tool for constructing cyclic subspace codes. In this letter, we construct some Sidon spaces by using primitive elements and the roots of some irreducible polynomials over finite fields. Let q be a prime power, k, m, n be three positive integers and $ ho= lceil rac{m}{2k} ceil-1$, $ heta= lceil rac{n}{2m} ceil-1$. Based on these Sidon spaces and the union of some Sidon spaces, new cyclic subspace codes with size $ rac{3(q^{n}-1)}{q-1}$ and $ rac{ heta ho q^{k}(q^{n}-1)}{q-1}$ are obtained. The size of these codes is lager compared to the known constructions from [14] and [10].
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E106-A No.8 pp.1062-1066
- Publication Date
- 2023/08/01
- Publicized
- 2023/01/30
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.2022EAL2074
- Type of Manuscript
- LETTER
- Category
- Coding Theory
Authors
Xue-Mei LIU
Civil Aviation University of China
Tong SHI
Civil Aviation University of China
Min-Yao NIU
Beijing University of Posts and Telecommunications
Lin-Zhi SHEN
Civil Aviation University of China
You GAO
Civil Aviation University of China
Keyword
Latest Issue
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Xue-Mei LIU , Tong SHI , Min-Yao NIU, Lin-Zhi SHEN, You GAO, "New Constructions of Sidon Spaces and Cyclic Subspace Codes" in IEICE TRANSACTIONS on Fundamentals,
vol. E106-A, no. 8, pp. 1062-1066, August 2023, doi: 10.1587/transfun.2022EAL2074.
Abstract: Sidon space is an important tool for constructing cyclic subspace codes. In this letter, we construct some Sidon spaces by using primitive elements and the roots of some irreducible polynomials over finite fields. Let q be a prime power, k, m, n be three positive integers and $
ho= lceil rac{m}{2k}
ceil-1$, $ heta= lceil rac{n}{2m}
ceil-1$. Based on these Sidon spaces and the union of some Sidon spaces, new cyclic subspace codes with size $ rac{3(q^{n}-1)}{q-1}$ and $ rac{ heta
ho q^{k}(q^{n}-1)}{q-1}$ are obtained. The size of these codes is lager compared to the known constructions from [14] and [10].
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2022EAL2074/_p
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@ARTICLE{e106-a_8_1062,
author={Xue-Mei LIU , Tong SHI , Min-Yao NIU, Lin-Zhi SHEN, You GAO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={New Constructions of Sidon Spaces and Cyclic Subspace Codes},
year={2023},
volume={E106-A},
number={8},
pages={1062-1066},
abstract={Sidon space is an important tool for constructing cyclic subspace codes. In this letter, we construct some Sidon spaces by using primitive elements and the roots of some irreducible polynomials over finite fields. Let q be a prime power, k, m, n be three positive integers and $
ho= lceil rac{m}{2k}
ceil-1$, $ heta= lceil rac{n}{2m}
ceil-1$. Based on these Sidon spaces and the union of some Sidon spaces, new cyclic subspace codes with size $ rac{3(q^{n}-1)}{q-1}$ and $ rac{ heta
ho q^{k}(q^{n}-1)}{q-1}$ are obtained. The size of these codes is lager compared to the known constructions from [14] and [10].},
keywords={},
doi={10.1587/transfun.2022EAL2074},
ISSN={1745-1337},
month={August},}
Copy
TY - JOUR
TI - New Constructions of Sidon Spaces and Cyclic Subspace Codes
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1062
EP - 1066
AU - Xue-Mei LIU
AU - Tong SHI
AU - Min-Yao NIU
AU - Lin-Zhi SHEN
AU - You GAO
PY - 2023
DO - 10.1587/transfun.2022EAL2074
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E106-A
IS - 8
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - August 2023
AB - Sidon space is an important tool for constructing cyclic subspace codes. In this letter, we construct some Sidon spaces by using primitive elements and the roots of some irreducible polynomials over finite fields. Let q be a prime power, k, m, n be three positive integers and $
ho= lceil rac{m}{2k}
ceil-1$, $ heta= lceil rac{n}{2m}
ceil-1$. Based on these Sidon spaces and the union of some Sidon spaces, new cyclic subspace codes with size $ rac{3(q^{n}-1)}{q-1}$ and $ rac{ heta
ho q^{k}(q^{n}-1)}{q-1}$ are obtained. The size of these codes is lager compared to the known constructions from [14] and [10].
ER -
English
