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.

中文翻译：

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半局部环上的固定码的应用$$ {F _ {{p ^ m}}}​​ + v {F _ {{p ^ m}}}​​ $$

在本文中，我们研究了量子码超过\（{F _ {{P ^ M}}} \） ，这是从获得的（λ ₁ +λ ₂）上的半局部环-constacyclic码\（{F _ {{ p ^ m}}}​​ + v {F _ {{p ^ m}}}​​ \），其中v ² = 1，p是奇质数。我们分解一个（λ ₁ +λ ₂）-constacyclic代码超过\（{F _ {{P ^ M}}} + V {F _ {{P ^ M}}} \）成两个常循环码超过\（{F_ { {p ^ M}}} \）如（λ ₁ +λ ₂）和-constacyclic（λ ₁ -λ ₂）-constacyclic。我们给予的充分必要条件是（λ ₁+ v λ ₂）-constacyclic码超过\（{F _ {{P ^ M}}} + V {F _ {{P ^ M}}} \）包含其对偶。我们给出一些非二进制量子码的例子。