Name
Abstract | ||
|---|---|---|
Generalized Goppa codes are defined by a code locator set L of polynomials and a Goppa polynomial G(x). When the degree of all code locator polynomials in 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. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.1109/ISIT45174.2021.9517785 | 2021 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT) |
DocType | Citations | PageRank |
Conference | 0 | 0.34 |
References | Authors | |
0 | 4 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hedongliang Liu | 1 | 0 | 0.34 |
| Sabine Pircher | 2 | 0 | 0.34 |
| Alexander Zeh | 3 | 0 | 0.34 |
| Antonia Wachter-Zeh | 4 | 129 | 33.65 |