On self-dual and LCD double circulant codes over Fq+uFq+vFq+uvFq

doi:10.3969/j.issn.0253-2778.2018.11.004

Journal of University of Science and Technology of China ›› 2018, Vol. 48 ›› Issue (11): 890-897.DOI: 10.3969/j.issn.0253-2778.2018.11.004

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On self-dual and LCD double circulant codes over Fq+uFq+vFq+uvFq

LU Yaqi, SHI Minjia, WU Wenting, XIAO Aqing

Received:2018-02-04 Revised:2018-04-11 Accepted:2018-04-11 Online:2018-11-30 Published:2018-04-11
Contact: SHI Minjia
About author:LU Yaqi, female, born in 1994, master. Research field: Algebraic coding. E-mail: lyqSunshine8@163.com
Supported by:
Supported by National Natural Science Foundation of China (61672036), Excellent Youth Foundation of Natural Science Foundation of Anhui Province(1808085J20).

Abstract

Abstract: Double circulant codes of length 2n over a non-chain ring Fq+uFq+vFq+uvFq, u2=v2=0, uv=vu, were studied when q was a prime power. Exact enumerations of self-dual and LCD double circulant codes for a positive integer n were given. Using a distance-preserving Gray map, self-dual and LCD codes of length 8n over Fq were constructed when q was even. Using random coding and the Artin conjecture, the modified Varshamov-Gilbert bounds were derived on the relative distance of the codes considered, building on exact enumeration results for given n and q.

Key words: double circulant codes, self-dual codes, LCD codes, Artin conjecture

CLC Number:

TP391

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On self-dual and LCD double circulant codes over Fq+uFq+vFq+uvFq

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