Construction of self-dual binary \([2^{2k},2^{2k-1},2^k]\)-codes

• Date: 2016
• Main Authors: Hannusch, Carolin, Lakatos, Piroska
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2016
• Subjects: Reed > Muller code; Generalized Reed > Muller code; radical; self-dual code; group algebra; Jacobson radical; 94B05; 11T71; 20C05
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/25
• Journal Title: Algebra and Discrete Mathematics

The binary Reed-Muller code \({\rm RM}(m-k,m)\) corresponds to the \(k\)-th power of the radical of \(GF(2)[G],\) where \(G\) is an elementary abelian group of order \(2^m \) (see~\cite{B}). Self-dual RM-codes (i.e. some powers of the radical of the previously mentioned group algebra) exist only for...