Weight distributions of two classes of linear codes with five or six weights
Linear codes with few weights have been an interesting subject of study for many years, as these codes have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, two classes of five-weight or six-weight linear codes over Fp are constr...
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| Published in | Discrete mathematics Vol. 345; no. 7; p. 112881 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.07.2022
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0012-365X 1872-681X |
| DOI | 10.1016/j.disc.2022.112881 |
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| Abstract | Linear codes with few weights have been an interesting subject of study for many years, as these codes have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, two classes of five-weight or six-weight linear codes over Fp are constructed and their weight distributions are determined by means of exponential sums. In one case, there are some almost optimal codes with respect to the Griesmer bound, which are in fact optimal according to the online code tables. |
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| AbstractList | Linear codes with few weights have been an interesting subject of study for many years, as these codes have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, two classes of five-weight or six-weight linear codes over Fp are constructed and their weight distributions are determined by means of exponential sums. In one case, there are some almost optimal codes with respect to the Griesmer bound, which are in fact optimal according to the online code tables. |
| ArticleNumber | 112881 |
| Author | Jin, Wengang Du, Xiaoni Zhang, Xina |
| Author_xml | – sequence: 1 givenname: Xina orcidid: 0000-0002-0851-1265 surname: Zhang fullname: Zhang, Xina email: zhangxina11@163.com – sequence: 2 givenname: Xiaoni surname: Du fullname: Du, Xiaoni email: ymldxn@126.com – sequence: 3 givenname: Wengang surname: Jin fullname: Jin, Wengang email: jinwengang0110@126.com |
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| Cites_doi | 10.1587/transfun.2020SDP0003 10.1007/s10623-016-0222-7 10.1016/j.ffa.2019.02.001 10.4064/aa-83-3-241-251 10.1006/ffta.2001.0348 10.4064/aa-86-3-217-226 10.1016/j.disc.2016.09.003 10.1109/LCOMM.2015.2455032 10.1109/TIT.2007.896886 10.1007/s10623-016-0267-7 10.1109/TIT.2015.2473861 |
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| Keywords | Linear codes Weight distributions Weil sums Almost optimal codes |
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| Title | Weight distributions of two classes of linear codes with five or six weights |
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