Generalized Goppa codes are defined by a code locator set $\mathcal{L}$ of polynomials and a Goppa polynomial $G(x)$. When the degree of all code locator polynomials in $\mathcal{L}$ is one, generalized Goppa codes are classical Goppa codes. In this work, binary generalized Goppa codes are investigated. First, a parity-check matrix for these codes with code locators of any degree is derived. A careful selection of the code locators leads to a lower bound on the minimum Hamming distance of generalized Goppa codes which improves upon previously known bounds. A quadratic-time decoding algorithm is presented which can decode errors up to half of the minimum distance. Moreover, interleaved generalized Goppa codes are introduced and a joint decoding algorithm is presented which can decode errors beyond half the minimum distance with high probability.

翻译：通用的 Goppa 代码由一个代码定位器定义 $\ mathcal{L} $( mathcal{L} $) 。 当所有代码定位器在$\ mathcal{L} $( x) $( $) 中的水平为一时, 通用的 Goppa 代码为古典的 Goppa 代码。 在此工作中, 对二进制通用的 Goppa 代码进行了调查 。 首先, 得出了这些代码与任何级别代码定位器的对等检查矩阵 。 仔细选择代码定位器可以降低通用的 Goppa 代码在先前已知界限上改进的最小宽度距离的宽度 。 演示了一种四进制时间解码算法, 可以解码错误到最小距离的一半 。 此外, 引入了内部通用的 Goppa 代码, 并提出了联合解码算算法, 可以解码超过一半的最小距离, 高概率 。