Quantum codes from constacyclic codes over

Bo Kong; Xiying Zheng

doi:10.1140/epjqt/s40507-023-00160-7

EPJ

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2023 Impact factor 5.8

Open Access

EPJ Quantum Technol. (2023) 10: 3
https://doi.org/10.1140/epjqt/s40507-023-00160-7

Research

Quantum codes from constacyclic codes over $S_{k}$ $S_{k}$

Bo Kong¹^a and Xiying Zheng²^b

¹ School of Statistics and Mathematics, Henan Finance University, 450046, Zhengzhou, Henan, China
² Faculty of Engineering, Huanghe Science and Technology College, 450063, Zhengzhou, Henan, China

^a kongbo666@163.com
^b zxyccnu@163.com

Received: 11 June 2022
Accepted: 25 January 2023
Published online: 6 February 2023

Abstract

Let $S_{k} = F_{q} [u_{1}, u_{2}, \dots, u_{k}] / 〈 u_{i}^{3} = u_{i}, u_{i} u_{j} = u_{j} u_{i} = 0 〉$ $S_{k}={\mathbb{F}}_{q}[u_{1},u_{2},\ldots ,u_{k}]/\langle u^{3}_{i}=u_{i},u_{i}u_{j}=u_{j}u_{i}=0 \rangle$ , where $1 \leq i, j \leq k$ $1\leq i,j\leq k$ , $q = p^{m}$ $q=p^{m}$ , p is an odd prime. First, we define two new Gray maps $ϕ_{k}$ $\phi _{k}$ and $φ_{k}$ $\varphi _{k}$ , and study their Gray images. Further, we determine the structure of constacyclic codes and their dual codes, and give a necessary and sufficient conditions of constacyclic codes to contain their duals. Finally, we obtain some new quantum codes over $F_{q}$ $\mathbb{F}_{q}$ by using CSS construction, and compare the constructed codes better than the existing literature.

Mathematics Subject Classification: 94B05 / 94B15 / 94B60

Key words: Constacyclic codes / Quantum codes / Gray map / Dual-containing codes / CSS construction

© The Author(s) 2023

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