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Maximal entanglement EAQECCs from cyclic and constacyclic codes over \({\mathbb {F}}_q+v_1{\mathbb {F}}_q+\cdots +v_{s-1}{\mathbb {F}}_q\)

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Abstract

Let \(R_{s-1}={\mathbb {F}}_q+v_1{\mathbb {F}}_q+\cdots +v_{s-1}{\mathbb {F}}_q\) be a finite non-chain ring, where q is an odd prime power, \(v_i^2=v_i, v_iv_j=v_jv_i=0\) for \(1\le i,j\le s-1\). In this paper, a class of maximal entanglement (ME) entanglement-assisted quantum error-correcting codes (EAQECCs) are obtained from Gray images of cyclic codes over \(R_{s-1}\). By a special Gray map, a class of maximal entanglement and maximum distance separable EAQECCs (ME-MDS EAQECCs) are constructed from Gray images of \((1-2v_1)\)-constacyclic codes over \(R_1={\mathbb {F}}_q+v_1{\mathbb {F}}_q\), where \(v_1^2=v_1\). Furthermore, some new ME EAQECCs are tabulated by comparing with some known EAQECCs.

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Data availability

The datasets generated during the current study are not publicly available due to the computational algorithm for searching good entanglement-assisted quantum error-correcting codes but are available from the corresponding author on reasonable request.

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Acknowledgements

This research is supported by the National Natural Science Foundation of China (Nos. 12071264, 11701336, 11626144, 11671235), the Shandong Provincial Natural Science Foundation under Grant (No. ZR2021QA047) and IC Program of Shandong Institutions of Higher Learning For Youth Innovative Talents.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shandong University of Technology, Zibo, 255000, People’s Republic of China

    Yaozong Zhang, Ying Liu, Xiaotong Hou, Jian Gao & Fanghui Ma

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  1. Yaozong Zhang
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Correspondence to Jian Gao.

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Zhang, Y., Liu, Y., Hou, X. et al. Maximal entanglement EAQECCs from cyclic and constacyclic codes over \({\mathbb {F}}_q+v_1{\mathbb {F}}_q+\cdots +v_{s-1}{\mathbb {F}}_q\). Quantum Inf Process 21, 333 (2022). https://doi.org/10.1007/s11128-022-03685-5

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