On the Number of Self-Dual Bases of GF(q m ) Over GF(q)

DOI10.2307/2048357zbMath0698.12015OpenAlexW2013573121MaRDI QIDQ3475350

Scott A. Vanstone, Dieter Jungnickel, Alfred J. Menezes

Publication date: 1990

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2048357

zbMATH Keywords

normal basesorthogonal circulant matricesself-dual basestrace orthogonal basis

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Finite fields (field-theoretic aspects) (12E20) Structure theory for finite fields and commutative rings (number-theoretic aspects) (11T30)

Related Items (20)

Rank-metric codes and their duality theory ⋮ A note on the distribution of self-dual normal bases generators of finite fields under trace map ⋮ Further results on LCD generalized Gabidulin codes ⋮ Almost weakly self-dual bases for finite fields ⋮ Some results on uniform arithmetic circuit complexity ⋮ Guest editorial: Special issue in honor of Scott A. Vanstone ⋮ A twisted Yu construction, Harish-Chandra characters, and endoscopy ⋮ New constructions of optimal binary LCD codes ⋮ Paley-like graphs over finite fields from vector spaces ⋮ A new characterization of dual bases in finite fields and its applications ⋮ Covariant mutually unbiased bases ⋮ Rank-metric complementary dual codes ⋮ Normal bases and their dual-bases over finite fields ⋮ Construction of self-dual normal bases and their complexity ⋮ Application of \(\mathcal{T}\)-direct codes in multiple-rate codes ⋮ A note on orthogonal circulant matrices over finite fields ⋮ Some important results on 𝒯-Direct codes ⋮ Construction of LCD-MRD codes of length n > N ⋮ Trace-orthogonal normal bases ⋮ Generalized AG codes and generalized duality

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