|
|||||
 |
|
|
|
|
|
|
|
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 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. |
PDF Access Denied
We have not been able to recognize your IP address
18.97.9.170
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for USD 30.00:
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 |
|
