A method for constructing self-dual codes over \(\mathbb {Z}_{2^m}\)
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- 作者：Sunghyu Han (1)
1. School of Liberal Arts ; Korea University of Technology and Education ; Cheonan聽 ; 330-708 ; Republic of Korea - 关键词：Building ; up construction ; Self ; dual code ; $${\mathbb Z}_{4}$$ Z 4 code ; $${\mathbb Z}_{2^m}$$ Z 2 m code ; 94B05 ; 94B60
- 刊名：Designs, Codes and Cryptography
- 出版年：2015
- 出版时间：May 2015
- 年：2015
- 卷：75
- 期：2
- 页码：253-262
- 全文大小：174 KB
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- 刊物主题：Mathematics
Combinatorics
Coding and Information Theory
Data Structures, Cryptology and Information Theory
Data Encryption
Discrete Mathematics in Computer Science
Information, Communication and Circuits - 出版者：Springer Netherlands
- ISSN：1573-7586
文摘
There are several methods for constructing self-dual codes over various rings. Among them, the building-up method is a powerful method, and it can be applied to self-dual codes over finite fields and several rings. Recently, Alfaro and Dhul-Qarnayn (Des Codes Cryptogr, doi:10.1007/s10623-013-9873-9) proposed a method for constructing self-dual codes over \({\mathbb F}_{q}[u]/(u^{t})\) . Their approach is a building-up approach that uses the matrix form. In this paper, we use the matrix form to develop a building-up approach for constructing self-dual codes over \({\mathbb Z}_{2^m} (m \ge 1)\) , which have not been considered thus far.