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Cyclic codes over the ring F2+uF2+vF2.

Cyclic codes over the ring F2+uF2+vF2.

Authors :
Samei, Karim
Alimoradi, Mohammad Reza
Source :
Computational & Applied Mathematics; Jul2018, Vol. 37 Issue 3, p2489-2502, 14p
Publication Year :
2018

Abstract

In this paper, we study linear and cyclic codes over the ring F2+uF2+vF2<inline-graphic></inline-graphic>. The ring F2+uF2+vF2<inline-graphic></inline-graphic> is the smallest non-Frobenius ring. We characterize the structure of cyclic codes over the ring R=F2+uF2+vF2<inline-graphic></inline-graphic> using of the work Abualrub and Saip (Des Codes Cryptogr 42:273-287, <xref>2007</xref>). We study the rank and dual of cyclic codes of odd length over this ring. Specially, we show that the equation |C||C⊥|=|R|n<inline-graphic></inline-graphic> does not hold in general for a cyclic code C of length n over this ring. We also obtain some optimal binary codes as the images of cyclic codes over the ring F2+uF2+vF2<inline-graphic></inline-graphic> under a Gray map, which maps Lee weights to Hamming weights. Finally, we give a condition for cyclic codes over R that contains its dual and find quantum codes over F2<inline-graphic></inline-graphic> from cyclic codes over the ring F2+uF2+vF2<inline-graphic></inline-graphic>. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
01018205
Volume :
37
Issue :
3
Database :
Complementary Index
Journal :
Computational & Applied Mathematics
Publication Type :
Academic Journal
Accession number :
130626934
Full Text :
https://doi.org/10.1007/s40314-017-0460-y