Construction of self-dual binary [2²ⁿ,2²ⁿ⁻¹,2ⁿ]-codes

• Published in: Algebra and Discrete Mathematics
• Date: 2016
• Main Authors: Hannusch, C., Lakatos, P.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2016
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/155203
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Construction of self-dual binary [2²ⁿ,2²ⁿ⁻¹,2ⁿ]-codes / C. Hannusch, P. Lakatos // Algebra and Discrete Mathematics. — 2016. — Vol. 21, № 1. — С. 59-68. — Бібліогр.: 15 назв. — англ.

The binary Reed-Muller code RM(m−n,m) corresponds to the n-th power of the radical of GF(2)[G], where G is an elementary abelian group of order 2m. Self-dual RM-codes (i.e. some powers of the radical of the previously mentioned group algebra) exist only for odd m. The group algebra approach enables...