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Orthogonality
from group characters
Steven T. Dougherty and Sara Myers
Vol. 14 (2021), No. 4, 555–570
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Abstract |
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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 and any subgroups and of with , there exists an orthogonality that gives . The second uses a counting argument to show that the additive group of the finite field with any duality 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. |
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Keywords
self-dual codes, group characters, orthogonality
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Mathematical Subject Classification 2010
Primary: 11T71, 94B05
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Milestones
Received: 31 May 2018
Revised: 6 February 2021
Accepted: 31 March 2021
Published: 23 October 2021
Communicated by Kenneth S. Berenhaut
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Authors |
| Steven T. Dougherty | |
| Department of Mathematics University of Scranton Scranton, PA United States |
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| Sara Myers | |
| Department of Mathematics University of Scranton Scranton, PA United States |
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