Weight Distribution of a Class of Linear Codes
Summary :
Linear codes with a few weights have many applications in secret sharing schemes, authentication codes, association schemes and strongly regular graphs, and they are also of importance in consumer electronics, communications and data storage systems. In this paper, based on the theory of defining sets, we present a class of five-weight linear codes over $mathbb{F}_p$(p is an odd prime), which include an almost optimal code with respect to the Griesmer bound. Then, we use exponential sums to determine the weight distribution.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E104-A No.2 pp.399-403
- Publication Date
- 2021/02/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.2020SDP0003
- Type of Manuscript
- Special Section PAPER (Special Section on Signal Design and Its Applications in Communications)
- Category
- Coding Theory
Authors
Xina ZHANG
Northwest Normal University,Guilin University of Electronic Technology
Xiaoni DU
Northwest Normal University
Rong WANG
Northwest Normal University
Fujun ZHANG
Northwest Normal University
Keyword
Latest Issue
Copyrights notice of machine-translated contents
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.
Cite this
Copy
Xina ZHANG, Xiaoni DU, Rong WANG, Fujun ZHANG, "Weight Distribution of a Class of Linear Codes" in IEICE TRANSACTIONS on Fundamentals,
vol. E104-A, no. 2, pp. 399-403, February 2021, doi: 10.1587/transfun.2020SDP0003.
Abstract: Linear codes with a few weights have many applications in secret sharing schemes, authentication codes, association schemes and strongly regular graphs, and they are also of importance in consumer electronics, communications and data storage systems. In this paper, based on the theory of defining sets, we present a class of five-weight linear codes over $mathbb{F}_p$(p is an odd prime), which include an almost optimal code with respect to the Griesmer bound. Then, we use exponential sums to determine the weight distribution.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2020SDP0003/_p
Copy
@ARTICLE{e104-a_2_399,
author={Xina ZHANG, Xiaoni DU, Rong WANG, Fujun ZHANG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Weight Distribution of a Class of Linear Codes},
year={2021},
volume={E104-A},
number={2},
pages={399-403},
abstract={Linear codes with a few weights have many applications in secret sharing schemes, authentication codes, association schemes and strongly regular graphs, and they are also of importance in consumer electronics, communications and data storage systems. In this paper, based on the theory of defining sets, we present a class of five-weight linear codes over $mathbb{F}_p$(p is an odd prime), which include an almost optimal code with respect to the Griesmer bound. Then, we use exponential sums to determine the weight distribution.},
keywords={},
doi={10.1587/transfun.2020SDP0003},
ISSN={1745-1337},
month={February},}
Copy
TY - JOUR
TI - Weight Distribution of a Class of Linear Codes
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 399
EP - 403
AU - Xina ZHANG
AU - Xiaoni DU
AU - Rong WANG
AU - Fujun ZHANG
PY - 2021
DO - 10.1587/transfun.2020SDP0003
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E104-A
IS - 2
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - February 2021
AB - Linear codes with a few weights have many applications in secret sharing schemes, authentication codes, association schemes and strongly regular graphs, and they are also of importance in consumer electronics, communications and data storage systems. In this paper, based on the theory of defining sets, we present a class of five-weight linear codes over $mathbb{F}_p$(p is an odd prime), which include an almost optimal code with respect to the Griesmer bound. Then, we use exponential sums to determine the weight distribution.
ER -
English
