Binary Goppa code: Difference between revisions

Revision as of 18:53, 25 May 2013

Revision as of 17:56, 26 October 2013

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Binary Goppa codes viewed as a special case of Goppa codes have the interesting property that they correct full <math>\deg(g)</math> errors, while only <math>\deg(g)/2</math> errors in ternary and all other cases. Asymptotically, this error correcting capability meets the famous [[Gilbert–Varshamov bound]].

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 rank), the binary Goppa codes are used in several [[post-quantum]] [[cryptosystem|cryptosystems]]s, notably [[McEliece cryptosystem]] and [[Niederreiter cryptosystem]].

==References==