Let $ \mathbb{F}_{q^t} $ be a finite field of cardinality $ q^t $, where $ q $ is a power of a prime number $ p $ and $ t\geq 1 $ is a positive integer. Firstly, a family of cyclic $ \mathbb{F}_q $-linear $ \mathbb{F}_{q^t} $-codes of length $ n $ is given, where $ n $ is a positive integer coprime to $ q $. Then according to the structure of this kind of codes, we construct $ 60 $ optimal cyclic $ \mathbb{F}_q $-linear $ \mathbb{F}_{q^2} $-codes which have the same parameters as the MDS codes over $ \mathbb{F}_{q^2} $.

中文翻译：

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一些最优的循环$ \ mathbb {F} _q $ -linear $ \ mathbb {F} _ {q ^ t} $代码

令$ \ mathbb {F} _ {q ^ t} $为基数的有限域$ q ^ t $，其中$ q $是素数的幂$ p $，而$ t \ geq 1 $是正数整数。首先，给出一个循环的$ \ mathbb {F} _q $ -linear $ \ mathbb {F} _ {q ^ t} $长度为$ n $的代码，其中$ n $是对$的正整数互质q $。然后根据这种代码的结构，我们构造$ 60 $最优循环$ \ mathbb {F} _q $ -linear $ \ mathbb {F} _ {q ^ 2} $ -code，它们的参数与MDS代码超过$ \ mathbb {F} _ {q ^ 2} $。