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

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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: January 2014

Published: May 2016

Abstract/ Introduction Related Papers Cited by

Abstract

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 ${\rm GR}({p^2},s)$.
- Self-dual codes,
- cyclic codes,
- codes over rings,
- Galois rings,
- Hermitian inner product.
Mathematics Subject Classification:Primary: 94B15, 94B60; Secondary: 13B25.
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