On a Goppa code whose structure polynomial has coefficients in the symbol field, the Frobenius acts. Its fixed codewords form a subcode. Deleting the naturally occurred redundance, we obtain a new code. It is proved that these new codes approach the Gilbert-Varshamov bound. It is also proved that these codes can be decoded within $O(n^2(\logn)^a)$ operations in the symbol field, which is usually much small than the location field, where $n$ is the codeword length, and $a$ a constant determined by the polynomial factorization algorithm.

翻译：对于结构多项式系数位于符号域中的古帕码，弗罗贝尼乌斯自同态作用于其上。其固定码字构成一个子码，通过删除自然产生的冗余，我们得到一种新码。本文证明这些新码逼近吉尔伯特-瓦尔沙莫夫界，同时证明这些码可在符号域中通过$O(n^2(\log n)^a)$次运算完成译码（通常符号域远小于位置域），其中$n$为码字长度，$a$为由多项式因式分解算法确定的常数。