On self-dual cyclic codes of length $p^a$ over $GR(p^2,s)$

Somphong  Jitman; San Ling; Ekkasit  Sangwisut

doi:10.3934/amc.2016004

Article Contents

2016, Volume 10, Issue 2: 255-273. Doi: 10.3934/amc.2016004

This issue Previous Article On the ideal associated to a linear code Next Article Constructing strongly-MDS convolutional codes with maximum distance profile

On self-dual cyclic codes of length $p^a$ over $GR(p^2,s)$

1.
Department of Mathematics, Faculty of Science, Silpakorn University, Nakhon Pathom 73000
2.
Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371
3.
Department of Mathematics and Statistics, Faculty of Science, Thaksin University, Phatthalung Campus, Phatthalung 93110

Received: December 31, 2013

Published: April 2016

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Abstract

In this paper, cyclic codes over the Galois ring ${\rm GR}({p^2},s)$ are studied. The main result is the characterization and enumeration of Hermitian self-dual cyclic codes of length $p^a$ over ${\rm GR}({p^2},s)$. Combining with some known results and the standard Discrete Fourier Transform decomposition, we arrive at the characterization and enumeration of Euclidean self-dual cyclic codes of any length over ${\rm GR}({p^2},s)$.

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Mathematics Subject Classification: Primary: 94B15, 94B60; Secondary: 13B25.

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