In this paper, we introduce \(\omega\)-constacyclic Type II duadic codes over \({\mathbb {F}}_4\) of length \(n=3p^t\), where p is a prime number, \(p \equiv 1\) (mod 6), and give their main properties. We also obtain a splitting of n such that extended \(\omega\)-constacyclic duadic codes are Hermitian self-dual. Moreover, we provide some examples by extended \(\omega\)-constacyclic duadic codes.

中文翻译：

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超出$$ {\ mathbb {F}} _ 4 $$ F 4的同位双偶编码

在本文中，我们介绍了长度为\（n = 3p ^ t \）的\（{\ mathbb {F}} _ 4 \）上的\（\ omega \）-常数II型双偶代码，其中p是质数，\（p \ equiv 1 \）（mod 6），并给出其主要属性。我们还获得了n的分裂，使得扩展的\（\ omega \）-常数双偶编码是Hermitian自对偶的。此外，我们通过扩展的\（\ omega \）-常数双偶数代码提供了一些示例。