Asymmetric quantum codes from skew cyclic codes over B1

Skew cyclic codes over Bk = Fpr [v1, ..., vk]/〈vi2 − vi, vivj – vjvi〉 have been studied by Irwansyah et al in 2018. In this paper we use B1 = Fp2 [v]/〈v2 – v〉 and the Gray map φ : B1→Fp22 defined by φ(a + bv) = (a, a + b) for all a + bv ∈ B1 and extend φ to Φ : B1n→Fp22n. If C is a skew cyclic code...

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Bibliographic Details
Main Authors: Muchtadi-Alamsyah, Intan, Irwansyah
Format: Conference Proceeding
Language:English
Subjects:
Asymmetry
Binary system
Codes
Online Access:Get full text
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Summary:Skew cyclic codes over Bk = Fpr [v1, ..., vk]/〈vi2 − vi, vivj – vjvi〉 have been studied by Irwansyah et al in 2018. In this paper we use B1 = Fp2 [v]/〈v2 – v〉 and the Gray map φ : B1→Fp22 defined by φ(a + bv) = (a, a + b) for all a + bv ∈ B1 and extend φ to Φ : B1n→Fp22n. If C is a skew cyclic code over B1, we can get Φ(C) ⊆ Fp22n a skew cyclic code if n is odd and a skew 2-quasicyclic code if n is even. Then by using the map S introduced by Ezerman et al in 2011, we get a (4n, p2k, 2d) additive code over Fp2 and we use this to construct an additive asymmetric quantum code.
ISSN:0094-243X
1551-7616
DOI:10.1063/1.5139134