论文标题
介绍三个最知名的GOPPA代码
Introducing Three Best Known Goppa Codes
论文作者
论文摘要
当前最著名的$ [239，21]，\，[240，21]，\，\ text {and} \，[241，21] $二进制线性代码分别具有最小距离98、98和99。在本文中，我们使用GOPPA多项式$（x^{17} + 1）^6，（x^{16} + x）^6，\ text {and}（x^{15} + 1）^6 $介绍了三个二进制GOPPA代码。 GOPPA代码为$ [239，21，103]，\，[240，21，104]，\，\，\ text {and} \，[241，21，104] $二进制线性代码。这些代码的最小距离比电流最佳的代码具有更大的距离，这些代码具有相应的长度和尺寸。此外，随着穿刺，缩短和扩展的技术，我们发现比具有各自的长度和尺寸的当前最佳代码更好的最小距离的派生代码。
The current best known $[239, 21], \, [240, 21], \, \text{and} \, [241, 21]$ binary linear codes have minimum distance 98, 98, and 99 respectively. In this article, we introduce three binary Goppa codes with Goppa polynomials $(x^{17} + 1)^6, (x^{16} + x)^6,\text{ and } (x^{15} + 1)^6$. The Goppa codes are $[239, 21, 103], \, [240, 21, 104], \, \text{and} \, [241, 21, 104]$ binary linear codes respectively. These codes have greater minimum distance than the current best known codes with the respective length and dimension. In addition, with the techniques of puncturing, shortening, and extending, we find more derived codes with a better minimum distance than the current best known codes with the respective length and dimension.
