Volume 30 Issue 1
Jan.  2021
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LI Tiantian, SHI Minjia, LIN Bo, WU Wenting. One and Two-Weight $\mathbb{Z}_{2}R_{2}$ Additive Codes[J]. Chinese Journal of Electronics, 2021, 30(1): 72-76. doi: 10.1049/cje.2020.10.011
 Citation: LI Tiantian, SHI Minjia, LIN Bo, WU Wenting. One and Two-Weight $\mathbb{Z}_{2}R_{2}$ Additive Codes[J]. Chinese Journal of Electronics, 2021, 30(1): 72-76.

# One and Two-Weight $\mathbb{Z}_{2}R_{2}$ Additive Codes

##### doi: 10.1049/cje.2020.10.011
Funds:

Provincial Natural Science Research Project of Anhui Colleges KJ2018A0030

Provincial Natural Science Research Project of Anhui Colleges KJ2019A0006

National Natural Science Foundation of China 12071001

National Natural Science Foundation of China 61672036

Excellent Youth Foundation of Natural Science Foundation of Anhui Province 1808085J20

Academic Fund for Outstanding Talents in Universities gxbjZD03

• Author Bio:

LI Tiantian   received the B.S. degree in mathematics from Anhui Normal University of China in 2003; the M.S. degree in mathematics from Anhui University, Hefei, in 2006, and the Ph.D. degree in electronics and information engineering from Anhui University, Hefei, in 2015. She has been teaching at the School of Mathematical Science of Anhui University since 2006. Her research interests include coding theory, cryptography and image processing

LIN Bo   is a undergraduate in Wendian School, Anhui University, his research interests include coding theory and cryptography

WU Wenting   received the B.S degree in mathematics from Anhui Normal University of China in 2004; the M.S degree in mathematics from East China Normal University, Shanghai, in 2007. She has been teaching at the School Mathematical Science of Anhui University since 2007. Her research interests include coding theory and cryptography

• Corresponding author: SHI Minjia   (corresponding author) received the B.S. degree in mathematics from Anqing Normal College of China in 2004; the M.S. degree in mathematics from Hefei University of Technology of China in 2007, and the Ph.D. degree in the Institute of Computer Network Systems from Hefei University of Technology of China in 2010. From August 2012 to August 2013, he was a visiting researcher with School of Physical & Mathematical Sciences, Nanyang Technological University, Singapore. In July-August 2016, he was a visiting researcher with Telecom Paris Tech, Paris, France. He has been teaching at the School of Mathematical Sciences of Anhui University since 2007. Since April 2012, he has been the Masters supervisor and Associate Professor with the School of Mathematical Sciences, Anhui University of China. He has been Ph.D. supervisor since 2014. Since 2017, he has been professor with the School of Mathematical Sciences, Anhui University of China. He is the author of over 80 journal papers and two books. His research interests include algebraic coding theory and cryptography. (Email: smjwcl.good@163.com)
• Accepted Date: 2020-07-24
• Publish Date: 2021-01-01
• This paper is devoted to the construction of one and two-weight $\mathbb{Z}_{2}R_{2}$ additive codes, where $R_{2}=\mathbb{F}_{2}[v]/\langle v.{4}\rangle$. It is a generalization towards another direction of $\mathbb{Z}_{2}\mathbb{Z}_{4}$ codes (S.T. Dougherty, H.W. Liu and L. Yu, "One weight $\mathbb{Z}_{2}\mathbb{Z}_{4}$ additive codes", \textit{Applicable Algebra in Engineering, Communication and Computing}, Vol.27, No.2, pp.123--138, 2016). A MacWilliams identity which connects the weight enumerator of an additive code over $\mathbb{Z}_{2}R_{2}$ and its dual is established. Several construction methods of one-weight and two-weight additive codes over $\mathbb{Z}_{2}R_{2}$ are presented. Several examples are presented to illustrate our main results and some open problems are also proposed.
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