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Construction of self-dual binary [2²ⁿ,2²ⁿ⁻¹,2ⁿ]-codes
Репозиторій DSpace/Manakin
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Construction of self-dual binary [2²ⁿ,2²ⁿ⁻¹,2ⁿ]-codes
Інший ID:
2010 MSC:94B05, 11T71, 20C05.
Посилання:
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.
Підтримка:
Research of the first author was partially supported by funding of EU’s FP7/2007-2013 grant No. 318202.
Дата:
2016
Переглядів:
699
Завантажень:
182
Анотація:
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 us to find a self-dual code for even m=2n in the radical of the previously mentioned group algebra with similarly good parameters as the self-dual RM codes.
