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A SPECIAL CLASS OF QUASI-CYCLIC CODES

Part of: Theory of error-correcting codes and error-detecting codes

Published online by Cambridge University Press:  10 August 2017

MINJIA SHI ,
JIE TANG ,
MAORONG GE ,
LIN SOK  and
PATRICK SOLÉ
MINJIA SHI*
Affiliation:
Key Laboratory of Intelligent Computing and Signal Processing, Anhui University, No. 3 Feixi Road, Hefei, Anhui Province 230039, PR China National Mobile Communications Research Laboratory, Southeast University, Nanjing, 210096, PR China School of Mathematical Sciences, Anhui University, Hefei, Anhui, 230601, PR China email smjwcl.good@163.com
JIE TANG
Affiliation:
School of Mathematical Sciences, Anhui University, Hefei, Anhui, 230601, PR China email Lucytang1208@163.com
MAORONG GE
Affiliation:
School of Mathematical Sciences, Anhui University, Hefei, Anhui, 230601, PR China email ge1968@163.com
LIN SOK
Affiliation:
School of Mathematical Sciences, Anhui University, Hefei, Anhui, 230601, PR China Department of Mathematics, Royal University of Phnom Penh, 12156 Phnom Penh, Cambodia email sok.lin@rupp.edu.kh
PATRICK SOLÉ
Affiliation:
CNRS/LAGA, Université Paris 8, 93 526 Saint-Denis, France email sole@enst.fr
*
✉ smjwcl.good@163.com
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Abstract

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We study a special class of quasi-cyclic codes, obtained from a cyclic code over an extension field of the alphabet field by taking its image on a basis. When the basis is equal to its dual, the dual code admits the same construction. We give some examples of self-dual codes and LCD codes obtained in this way.

Keywords

quasi-cyclic codescyclic codesself-dual codesLCD codes

MSC classification

Primary: 94B05: Linear codes, general
Secondary: 94B15: Cyclic codes
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 96 , Issue 3 , December 2017 , pp. 513 - 518
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

Footnotes

The first and the last two authors were supported by NNSF of China (61672036), Technology Foundation for Selected Overseas Chinese Scholars, Ministry of Personnel of China (05015133), the Open Research Fund of National Mobile Communications Research Laboratory, Southeast University (2015D11) and Key Projects of Support Program for Outstanding Young Talents in Colleges and Universities (gxyqZD2016008). The fourth author was supported by China Postdoctoral Science Foundation funded project (2016M601991).

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