The polycyclic codes over the finite field $ \mathbb{F}_q $

This article extended the properties of the idempotent generator of cyclic codes to polycyclic codes over the finite field $ \mathbb{F}_q $. In addition, the check matrix of polycyclic codes was provided over $ \mathbb{F}_q $. Specifically, it has been proven that the constacyclic code is an $ {{{\r...

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التفاصيل البيبلوغرافية
الحاوية / القاعدة:AIMS Mathematics
المؤلف الرئيسي: Wei Qi
التنسيق: مقال
اللغة:الإنجليزية
منشور في: AIMS Press 2024-10-01
الموضوعات:
polycyclic codes
idempotent generator
check matrix
$ {{{\rm{mds}}}} $ codes
الوصول للمادة أونلاين:https://www.aimspress.com/article/doi/10.3934/math.20241439?viewType=HTML
الوصف
الملخص:This article extended the properties of the idempotent generator of cyclic codes to polycyclic codes over the finite field $ \mathbb{F}_q $. In addition, the check matrix of polycyclic codes was provided over $ \mathbb{F}_q $. Specifically, it has been proven that the constacyclic code is an $ {{{\rm{MDS}}}} $ code over $ \mathbb{F}_q $ if and only if its annihilator dual code is also an $ {{{\rm{MDS}}}} $ code. Finally, we have provided some examples of good codes.
تدمد:2473-6988

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