Faut Please help us clarify the article. In non-binary cases a separate error correction polynomial has to be computed as well. The vector space is a subspace of the function field of X. 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 includes a list of referencesrelated reading or external linksbut its sources remain unclear because it lacks inline citations.
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Coding theory Algebraic curves Finite fields. Please help to improve this article by introducing more precise citations. Goppa code The following shows goppx the parameters of the code relate to classical parameters of linear systems of divisors D on C cf. In non-binary cases a separate error correction polynomial has to be computed as well.
Such codes were introduced by Valerii Denisovich Goppa. They should not be confused with Binary Goppa codes that are used, for instance, in the McEliece cryptosystem.
Binary Goppa codes have interesting properties suitable for cryptography in McEliece-like cryptosystems and similar setups. This article has multiple issues. Binary Goppa code This page was last edited on gopa Octoberat Asymptotically, this error correcting capability meets the famous Gilbert—Varshamov bound. Please help improve it or discuss these issues on the talk page. 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.
From Wikipedia, the free encyclopedia. Views Read Edit View history. Binary Goppa code — Wikipedia This article includes a list of referencesrelated reading goppa external linksbut its sources remain unclear because it lacks inline citations. In particular cases, they can have interesting extremal properties. Riemann—Roch theorem for more.
We usually denote a Goppa code by C DG. In mathematics gopppa 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, also providing a better fit for common usage in computers and telecommunication.
Please help us clarify the article. February Learn how and when to remove this template message. Patterson algorithm converts a syndrome to a gpppa of errors. There might be a discussion about this on the talk page. April Learn how and when to remove this template message. We now know all we need to define the Goppa code:. This article may be confusing or unclear to readers.
Vudokus Views Read Edit View history. We now know all we need to define the Goppa code:. They should not be confused with Binary Goppa codes that are used, for instance, in the McEliece cryptosystem. Views Read Edit View history.
Binary Goppa code