Due to their wide applications in communications, data storage and cryptography, linear codes have received much attention in the past decades. The objective of this paper is to construct a family of linear codes over \({\mathbb F}_{q}\), where q is a prime power. This family of codes has length (q^k − 1)t, dimension ek, where k ≥ 2 and e, t are arbitrary integers with 2 ≤ e ≤ t . In some cases, this class of linear codes is distance-optimal with respect to the Griesmer bound. The weight distribution of this family of linear codes is also determined. Furthermore, we show that our codes can be used to construct secret sharing schemes with interesting access structures and strongly regular graphs with new parameters.

中文翻译：

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具有灵活参数的距离最优最小线性代码系列

由于线性代码在通信，数据存储和密码学中的广泛应用，在过去的几十年中，线性代码受到了广泛的关注。本文的目的是在\（{\ mathbb F} _ {q} \）上构造一个线性代码族，其中q是素数。码的该系列具有长度（q ^ķ - 1）吨，尺寸EK，其中ķ ≥2和ë，吨与2≤任意整数È ≤吨。在某些情况下，此类线性代码相对于Griesmer边界距离最优。还确定了该系列线性代码的权重分布。此外，我们证明了我们的代码可用于构造具有有趣访问结构和具有新参数的强规则图的秘密共享方案。