Generalization of Lower Bound on the Minimum Distanceand the Upper Bound on the Number of Parity CheckDigits for Goppa Codes

Feng Gui-liang

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Generalization of Lower Bound on the Minimum Distanceand the Upper Bound on the Number of Parity CheckDigits for Goppa Codes

更新时间：2025-12-08

- Generalization of Lower Bound on the Minimum Distanceand the Upper Bound on the Number of Parity CheckDigits for Goppa Codes
- Acta Electronica Sinica Issue 2, Pages: 66-72(1983)
- 作者机构：
  
  上海计算技术研究所
- 作者简介：
- 基金信息：
- DOI：
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- Published：1983
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[1]冯贵良.Goppa码的最小距离下限和维数上限的扩张[J].电子学报,1983(02):66-72.

Feng Gui-liang. Generalization of Lower Bound on the Minimum Distanceand the Upper Bound on the Number of Parity CheckDigits for Goppa Codes[J]. Acta Electronica Sinica, 1983, (2): 66-72.
[1]冯贵良.Goppa码的最小距离下限和维数上限的扩张[J].电子学报,1983(02):66-72. DOI：

Feng Gui-liang. Generalization of Lower Bound on the Minimum Distanceand the Upper Bound on the Number of Parity CheckDigits for Goppa Codes[J]. Acta Electronica Sinica, 1983, (2): 66-72. DOI：

摘要

给定一个Goppa码

如何求出它的最小距离和维数问题

至今没有解决。众所周知

生成多项式G（z）

位置集L（?）GF（q

）

在GF（q）上的Goppa码具有最小距离d≥degG（z）+1和一致校验位数目n-k≤m·degG（z）。对于二元码

令（?）是能整除G（z）的最低完全平方多项式

则d≥degG（z）+1。本文推广了已有结果

指出Goppa码的最小距离和维数不仅与G（z）有关

而且与L有关。

Abstract

The problem of finding the minimum distance and the number of parity check digits for a given Goppa code has not been solved as yet. It is well known that the Goppa code over GF（q） with G（z） and L GF （qm） has its minimum distance d≥deg G（z） + 1 and its number of parity check digits n-k≤m deg G（z）

and in the binary case

let G（z） be the lowest degree perfect square which is divisible by G（z）

then d≥-deg G（z） +1. In this paper

these results are generalized

and it is pointed out that the minimum distance and the number of parity check digits for a given Goppa code are related not only with G（z） but also with L.

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