Generator polynomials of cyclic expurgated or extended Goppa codes
<|reference_start|>Generator polynomials of cyclic expurgated or extended Goppa codes: Classical Goppa codes are a well-known class of codes with applications in code-based cryptography, which are a special case of alternant codes. Many papers are devoted to the search for Goppa codes with a cyclic extension or with a cyclic parity-check subcode. Let $\Bbb F_q$ be a finite field with $q=2^l$ elements, where $l$ is a positive integer. In this paper, we determine all the generator polynomials of cyclic expurgated or extended Goppa codes under some prescribed permutations induced by the projective general linear automorphism $A \in PGL_2(\Bbb F_q)$. Moreover, we provide some examples to support our findings.<|reference_end|>
@article{jia2024generator,
    title={Generator polynomials of cyclic expurgated or extended Goppa codes},
    author={Xue Jia, Fengwei Li, Huan Sun, Qin Yue},
    journal={arXiv preprint arXiv:2405.18023},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.18023},
    primaryClass={cs.IT math.IT}
}