Codes over local rings of order 16 and binary codes

Steven T.  Dougherty; Esengül  Saltürk; Steve  Szabo

doi:10.3934/amc.2016012

Article Contents

2016, Volume 10, Issue 2: 379-391. Doi: 10.3934/amc.2016012

This issue Previous Article The geometric structure of relative one-weight codes Next Article Non-existence of a ternary constant weight $(16,5,15;2048)$ diameter perfect code

Codes over local rings of order 16 and binary codes

1.
Department of Mathematics, University of Scranton, Scranton, PA 18510
2.
Department of Mathematics and Statistics, Eastern Kentucky University Richmond, KY 40475

Received: August 2014

Revised: February 2015

Published: May 2016

Abstract / Introduction Related Papers Cited by

Abstract

We study codes over the commutative local Frobenius rings of order 16 with maximal ideals of size 8. We define a weight preserving Gray map and study the images of these codes as binary codes. We study self-dual codes and determine when they exist.

Keywords:

Codes over rings,
Gray maps.

Mathematics Subject Classification: Primary: 11T71, 94B05; Secondary: 13H99.

Citation:

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