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

Published online by Cambridge University Press:  27 September 2016

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 [email protected]
JIAQI FENG
Affiliation:
School of Mathematical Sciences, Anhui University, Hefei, Anhui 230601, PR China email [email protected]
JIAN GAO
Affiliation:
School of Science, Shandong University of Technology, Zibo 255091, PR China email [email protected]
ADEL ALAHMADI
Affiliation:
Mathematics Department, King Abdulaziz University, Jeddah, Saudi Arabia email [email protected]
PATRICK SOLÉ
Affiliation:
CNRS/LTCI, University of Paris-Saclay, 75013 Paris, France email [email protected]
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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.

MSC classification

Type
Research Article
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

References

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