Abstract
In this paper, we study the quantum codes over \({F_{{p^m}}}\), which are obtained from (λ1 + λ2)-constacyclic codes over the semi local ring \({F_{{p^m}}} + v{F_{{p^m}}}\), where v2 = 1, p is odd prime. We decompose a (λ1 + λ2)-constacyclic code over \({F_{{p^m}}} + v{F_{{p^m}}}\) into two constacyclic codes over \({F_{{p^m}}}\) such as (λ1 + λ2)-constacyclic and (λ1–λ2)-constacyclic. We give the necessary and sufficient condition that the (λ1 + vλ2)-constacyclic codes over \({F_{{p^m}}} + v{F_{{p^m}}}\) contain their duals. We give some examples of non binary quantum codes.
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Acknowledgement
The first author is thankful to University Grant Commission (UGC), Govt. of India for financial support under Sr. No. 2061441025 with Ref No. 22/06/2014(i)EU-V.
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Bag, T., Dertli, A., Cengellenmis, Y. et al. Application of Constacyclic Codes Over the Semi Local Ring \({F_{{p^m}}} + v{F_{{p^m}}}\). Indian J Pure Appl Math 51, 265–275 (2020). https://doi.org/10.1007/s13226-020-0399-3
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DOI: https://doi.org/10.1007/s13226-020-0399-3