Decoding of (Interleaved) Generalized Goppa Codes

Hedongliang Liu, Sabine Pircher, Alexander Zeh, Antonia Wachter-Zeh

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

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.

Original languageEnglish
Title of host publication2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages664-669
Number of pages6
ISBN (Electronic)9781538682098
DOIs
StatePublished - 12 Jul 2021
Event2021 IEEE International Symposium on Information Theory, ISIT 2021 - Virtual, Melbourne, Australia
Duration: 12 Jul 202120 Jul 2021

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2021-July
ISSN (Print)2157-8095

Conference

Conference2021 IEEE International Symposium on Information Theory, ISIT 2021
Country/TerritoryAustralia
CityVirtual, Melbourne
Period12/07/2120/07/21

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