Valentijn, Ashley, “Goppa Codes and Their Use in the McEliece Cryptosystems” ( ). Syracuse University Honors Program Capstone. Ideas from algebraic geometry became useful in coding theory after Goppa’s to give a partial account of the interplay between one-point Goppa codes and. Goppa Codes. & the McEliece Cryptosystem scriptie voor het verkrijgen van de graad van doctorandus in de Wiskunde, aan de Faculteit der Exacte.

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Asymptotically, this error correcting capability meets the famous Gilbert—Varshamov bound. Retrieved from ” https: This article includes a list of referencesrelated reading or external linksbut its sources remain unclear because it lacks inline citations.

Binary Goppa codes have interesting properties suitable for cryptography in McEliece-like cryptosystems codex similar setups. We now know all we need to define the Goppa code:. Please help improve it or discuss these issues on the talk page. Please help gopoa clarify the article. We usually denote a Goppa code by C DG. Note that in binary case, locating the errors is sufficient to correct them, as there’s only one other value possible.

Goppa code

Riemann—Roch theorem for more. There might be a discussion about this on the talk page. This page was last edited on 16 Octoberat By using this site, you agree to the Terms of Use and Privacy Policy.


In mathematics and computer sciencethe binary Goppa code is an error-correcting code that belongs to the class of general Goppa codes originally described by Valerii Denisovich Goppabut the binary structure gives it several mathematical advantages over non-binary variants, codrs providing a better fit for common usage in computers and telecommunication.

Binary Goppa code

By using this site, you agree to the Terms of Use and Privacy Policy. In non-binary cases a separate error correction polynomial has to be computed as well. This page was last edited on 14 Novemberat The following shows how the parameters of the code relate to classical parameters of linear systems of divisors D on C cf.

Because of the high error correction capacity compared to code rate and form of parity-check matrix which is usually hardly distinguishable from a random binary matrix of full rankthe binary Goppa codes are used in several post-quantum cryptosystemsnotably McEliece cryptosystem and Niederreiter cryptosystem.

This article has multiple issues. April Learn how and when to remove this template message. They should goppx be confused with Binary Goppa codes that are used, for instance, in the McEliece cryptosystem.


Patterson algorithm converts a syndrome to a vector of errors. Views Read Edit View history.

Goppa codes – Semantic Scholar

Such codes were introduced by Valerii Denisovich Goppa. Retrieved from ” https: Coding theory Algebraic curves Finite fields. February Learn how and when to remove this template message.

Views Read Edit View history. From Wikipedia, the free encyclopedia. The vector space is a subspace of the function field of X.

Binary Goppa code – Wikipedia

Please help to improve this article by introducing more precise citations. The notation l D means the dimension of L D. From Wikipedia, the free encyclopedia. In particular cases, they can have interesting extremal properties. Wikipedia articles needing clarification from February All Wikipedia articles needing clarification Articles lacking in-text citations from April All articles lacking in-text citations Articles with multiple maintenance issues Articles containing proofs.

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