Almost weakly self-dual bases for finite fields
type: Item
instance of: scholarly article
title: Almost weakly self-dual bases for finite fields
zbMATH Open document ID: 0882.11067
author: Ilene H. Morgan
author: Gary L. Mullen
author: Miodrag Živković
published in: Applicable Algebra in Engineering, Communication and Computing
publication date: 1997-02-13T00:00:00Z
review text: It is well-known that polynomial self-dual bases for a finite field \(\text{GF}(q^n)\) over the ground field \(\text{GF}(q)\) never exist (which is unfortunate, since such bases would be very useful in constructing hardware devices for finite field multiplication called ``bit serial dual basis multipliers''). This fact has prompted the study of more general notions, in particular, that of weakly self-dual bases; see Chapter 4 of [\textit{D. Jungnickel}, Finite fields: structure and arithmetics, B. I.-Wissenschaftsverlag (1993; Zbl 0779.11058)] for background. The authors study a further generalization, namely almost weakly self-dual polynomial bases; essentially, these correspond to the polynomial bases associated with irreducible trinomials. Their results finish the classification of the polynomial bases with excess \(0\); the paper also contains some results on bases with larger excess.
Mathematics Subject Classification ID: 11T30
zbMATH DE Number: 978145
zbMATH Keywords: finite field
zbMATH Keywords: almost weakly self-dual polynomial bases
reviewed by: Dieter Jungnickel
MaRDI profile type: Publication
full work available at URL: s002000050049
OpenAlex ID: W2009212302
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DOI: 10.1007/S002000050049
description: scientific article; zbMATH DE number 978145