In coding theory, constructing codes with good parameters is one of the most important and fundamental problems. Though a great many of good codes have been produced, most of them are defined over alphabets of sizes equal to prime powers. In this paper, we provide a new explicit construction of $(q+1)$-ary nonlinear codes via algebraic function fields, where $q$ is a prime power. Our codes are constructed by evaluations of rational functions at all rational places of the algebraic function field. Compared with algebraic geometry codes, the main difference is that we allow rational functions to be evaluated at pole places. After evaluating rational functions from a union of Riemann-Roch spaces, we obtain a family of nonlinear codes over the alphabet $\mathbb{F}_{q}\cup \{\infty\}$. It turns out that our codes have better parameters than those obtained from MDS codes or good algebraic geometry codes via code alphabet extension and restriction.

翻译：在编译理论中,构建具有良好参数的代码是最重要的根本性问题之一。 虽然已经生成了大量好的代码, 但大多数都是在与主要力量相等的大小字母上定义的。 在本文中, 我们通过代数函数字段提供了一个新的明确的构建值为$( q+1) $- $- 非线性代码, 其中$q$是一个主要力量。 我们的代码是通过对代数函数字段所有合理位置的合理功能的评估来构建的。 与代数几何参数代码相比, 主要的区别是, 我们允许在极地评估合理功能。 在对里曼- 洛克空间联盟的合理功能进行评估后, 我们得到了一个非线性代码的组合, 而不是以 $\mathb{ F ⁇ q ⁇ ⁇ cup ⁇ infty ⁇ $。 事实证明, 我们的代码比从代数函数或良好的代数测法代码中得出的参数要好。