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Cyclic codes over the ring F2+uF2+vF2.
Cyclic codes over the ring F2+uF2+vF2.
- 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]
- Subjects :
- FROBENIUS algebras
EQUATIONS
BINARY codes
HAMMING weight
MATHEMATICS theorems
Subjects
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