A Family of Constacyclic Codes over F2m + uF2m and Its Application to Quantum Codes

TANG Yongsheng; YAO Ting; ZHU Shixin; KAI Xiaoshan

doi:10.1049/cje.2019.10.007

Volume 29 Issue 1

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TANG Yongsheng, YAO Ting, ZHU Shixin, et al., “A Family of Constacyclic Codes over F2m + uF2m and Its Application to Quantum Codes,” Chinese Journal of Electronics, vol. 29, no. 1, pp. 114-121, 2020, doi: 10.1049/cje.2019.10.007

Citation:

TANG Yongsheng, YAO Ting, ZHU Shixin, et al., “A Family of Constacyclic Codes over F_2^m + uF_2^m and Its Application to Quantum Codes,” Chinese Journal of Electronics, vol. 29, no. 1, pp. 114-121, 2020, doi: 10.1049/cje.2019.10.007

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A Family of Constacyclic Codes over F_2^m + uF_2^m and Its Application to Quantum Codes

doi: 10.1049/cje.2019.10.007

1.
School of Mathematics and Statistics, Hefei Normal University, Hefei 230601, China;
2.
School of Mathematics, Hefei University of Technology, Hefei 230601, China

Funds: This work is supported by the Natural Science Foundation of Anhui Province (No.1808085MA15), Key University Science Research Project of Anhui Province (No.KJ2018A0497, No.KJ2018A0584), and National Natural Science Foundation of China (No.61772168, No.61572168).

Received Date: 2018-04-23
Rev Recd Date: 2019-02-26
Publish Date: 2020-01-10

Abstract

Abstract

Let R be the ring F_2^m + uF_2^m, where u²=0. We introduce a Gray map from R to F₂²m and study (1 + u)-constacyclic codes over R. It is proved that the image of a (1 + u)-constacyclic code length n over R under the Gray map is a distance-invariant binary quasicyclic code of index m and length 2mn. We also prove that every code of length 2mn which is the Gray image of cyclic codes over R of length n is permutation equivalent to a binary quasi-cyclic code of index m. Furthermore, a family of quantum error-correcting codes obtained from the Calderbank-Shor-Steane (CSS) construction applied to (1 + u)-constacyclic codes over R.
- Constacyclic codes,
- Cyclic codes,
- Quasicyclic codes,
- Gray map,
- Quantum codes

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References(32)

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