Vol. 14, No. 4, 2021

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Orthogonality from group characters

Steven T. Dougherty and Sara Myers

Vol. 14 (2021), No. 4, 555–570
Abstract

We prove two major results about using group characters to define orthogonality for codes over abelian groups. The first is that for a finite commutative group G and any subgroups H and K of G with |H||K| = |G|, there exists an orthogonality that gives H = K. The second uses a counting argument to show that the additive group of the finite field 𝔽22k with any duality M has a self-dual code of length 1 and therefore of all lengths. Additionally, we give numerous examples of orthogonalities for specific groups and we give families of orthogonalities that apply to any finite commutative group.

Keywords
self-dual codes, group characters, orthogonality
Mathematical Subject Classification 2010
Primary: 11T71, 94B05
Milestones
Received: 31 May 2018
Revised: 6 February 2021
Accepted: 31 March 2021
Published: 23 October 2021

Communicated by Kenneth S. Berenhaut
Authors
Steven T. Dougherty
Department of Mathematics
University of Scranton
Scranton, PA
United States
Sara Myers
Department of Mathematics
University of Scranton
Scranton, PA
United States