  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. 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.
Finally, some code parameters and how they apply to the Classic McEliece
post-quantum cryptosystem are shown.
