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ON LINEAR COMPLEMENTARY DUAL FOUR CIRCULANT CODES

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

Published online by Cambridge University Press:  29 April 2018

HONGWEI ZHU Open the ORCID record for HONGWEI ZHU [Opens in a new window]  and
MINJIA SHI Open the ORCID record for MINJIA SHI [Opens in a new window]
HONGWEI ZHU
Affiliation:
School of Mathematical Sciences, Anhui University, Hefei, Anhui 230601, China email zhwgood66@163.com
MINJIA SHI*
Affiliation:
Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, Anhui University, No. 3 Feixi Road, Hefei, Anhui Province 230039, PR China School of Mathematical Sciences of Anhui University, Anhui 230601, PR China email smjwcl.good@163.com
*
✉smjwcl.good@163.com
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Abstract

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We study linear complementary dual four circulant codes of length $4n$ over $\mathbb{F}_{q}$ when $q$ is an odd prime power. When $q^{\unicode[STIX]{x1D6FF}}+1$ is divisible by $n$, we obtain an exact count of linear complementary dual four circulant codes of length $4n$ over $\mathbb{F}_{q}$. For certain values of $n$ and $q$ and assuming Artin’s conjecture for primitive roots, we show that the relative distance of these codes satisfies a modified Gilbert–Varshamov bound.

Keywords

four circulant codeslinear complementary dual (LCD) codesArtin’s conjectureChinese remainder theorem

MSC classification

Primary: 94B05: Linear codes, general
Secondary: 94B15: Cyclic codes
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 98 , Issue 1 , August 2018 , pp. 159 - 166
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

Footnotes

This research is supported by the National Natural Science Foundation of China (61672036), Technology Foundation for Selected Overseas Chinese Scholar, Ministry of Personnel of China (05015133) and Key Projects of Support Program for Outstanding Young Talents in Colleges and Universities (gxyqZD2016008).

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