A Theorem that GF (24m) has no Self-Complementary Normal Bases over GF (2) for Odd m

Masakatu MORII  Kyoki IMAMURA  

IEICE TRANSACTIONS (1976-1990)   Vol.E67   No.12   pp.655-656
Publication Date: 1984/12/25
Online ISSN: 
Print ISSN: 0000-0000
Type of Manuscript: LETTER
Category: Mathematics

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A self-complementary basis of a finite field corresponds to the orthonormal basis of a vector metric space. This paper presents a theorem that GF (24m) has no self-complementary normal bases over GF (2) if m is odd, which was recently conjectured by one of the present authors.