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ON THE SUPPORT WEIGHT DISTRIBUTION OF LINEAR CODES OVER THE RING $\mathbb{F}_{p}+u\mathbb{F}_{p}+\cdots +u^{d-1}\mathbb{F}_{p}$

Part of: Theory of error-correcting codes and error-detecting codes

Published online by Cambridge University Press:  27 September 2016

MINJIA SHI ,
JIAQI FENG ,
JIAN GAO ,
ADEL ALAHMADI  and
PATRICK SOLÉ
MINJIA SHI*
Affiliation:
Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, Anhui University, No. 3 Feixi Road, Hefei, Anhui Province 230039, PR China National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, PR China School of Mathematical Sciences, Anhui University, Hefei, Anhui 230601, PR China email smjwcl.good@163.com
JIAQI FENG
Affiliation:
School of Mathematical Sciences, Anhui University, Hefei, Anhui 230601, PR China email FengJQ1995@163.com
JIAN GAO
Affiliation:
School of Science, Shandong University of Technology, Zibo 255091, PR China email jiangao@mail.nankai.edu.cn
ADEL ALAHMADI
Affiliation:
Mathematics Department, King Abdulaziz University, Jeddah, Saudi Arabia email adelnife2@yahoo.com
PATRICK SOLÉ
Affiliation:
CNRS/LTCI, University of Paris-Saclay, 75013 Paris, France email patrick.sole@telecom-paristech.fr
*
✉ smjwcl.good@163.com
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Abstract

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Let $R=\mathbb{F}_{p}+u\mathbb{F}_{p}+u^{2}\mathbb{F}_{p}+\cdots +u^{d-1}\mathbb{F}_{p}$ , where $u^{d}=u$ and $p$ is a prime with $d-1$ dividing $p-1$ . A relation between the support weight distribution of a linear code $\mathscr{C}$ of type $p^{dk}$ over $R$ and the dual code $\mathscr{C}^{\bot }$ is established.

Keywords

codes over ringssupport weightsupport weight distribution

MSC classification

Primary: 94B05: Linear codes, general
Secondary: 94B15: Cyclic codes
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 95 , Issue 1 , February 2017 , pp. 157 - 163
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

References

Cui, J., ‘Support weight distribution of ℤ4 -linear codes’, Discrete Math. 247 (2002), 135–145.Google Scholar
Dougherty, S., Gulliver, A. and Oura, M., ‘Higher weights and graded rings for binary self-dual codes’, Discrete Appl. Math. 128 (2003), 251–261.CrossRefGoogle Scholar
Gao, J., ‘Note on support weight distribution of linear codes over F p + uF p ’, Bull. Aust. Math. Soc. 91 (2015), 345–350.Google Scholar
Kløve, T., ‘Support weight distribution of linear codes’, Discrete Math. 106 (1992), 311–316.Google Scholar
Simonis, J., ‘The effective length of subcodes’, Applic. Algebra Eng. Common. Computing 5 (1992), 371–377.Google Scholar
Wei, V. K., ‘Generalized Hamming weights for linear codes’, IEEE Trans. Inform. Theory 37 (1991), 1412–1418.Google Scholar