TANG Yongsheng, YAO Ting, ZHU Shixin, KAI Xiaoshan. A Family of Constacyclic Codes over F2m + uF2m and Its Application to Quantum Codes[J]. Chinese Journal of Electronics, 2020, 29(1): 114-121. doi: 10.1049/cje.2019.10.007
Citation: TANG Yongsheng, YAO Ting, ZHU Shixin, KAI Xiaoshan. A Family of Constacyclic Codes over F2m + uF2m and Its Application to Quantum Codes[J]. Chinese Journal of Electronics, 2020, 29(1): 114-121. doi: 10.1049/cje.2019.10.007

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

doi: 10.1049/cje.2019.10.007
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
  • Let R be the ring F2m + uF2m, 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.
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