Binary Goppa code

In mathematics and computer science, the binary Goppa code is an error-correcting code that belongs to the class of general Goppa codes originally…

Papers overview

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2011

Common cryptographic methods, especially Public Key Crypto Systems, PKCS based on difficulty to factor large integers or to…

2007

In this paper, by defining an irreducible Goppa code in terms of a single field element, we give a simple proof of the well known…

2001

We present a new family of binary codes derived from the family of classical Goppa codes. We generalize properties of Goppa codes…

1998

A new bound for the dimension of binary Goppa codes belonging to a specific subclass is given. This bound improves the well-known…

1997

We discuss parameters of Goppa (1970) codes, such as minimum distance, covering radius, distance distribution, and generalized…

1987

Based on a finite Fourier transform of codewords over the finite field GF (q^{m}) , some basic properties of the class of Goppa…

1984

A [55, 16, 19] binary Goppa code and some related codes are described. These codes are found to contain more codewords than any…

1984

1977

It is shown that i) erasures-and-errors decoding of Goppa codes can be done using O(n \log^{2} n) arithmetic operations, ii) long…

1976

Goppa showed that the performance of most "Goppa codes" approaches the Gilbert bound asymptotically, but their performance for…