Binary Goppa code: Difference between revisions

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==Construction and properties==

AAn irreducible binary Goppa code is defined by a [[polynomial]] <math>g(x)</math> of degree <math>t</math> over a [[finite field]] <math>GF(2^m)</math> with no repeated roots, and a sequence <math>L_1, ..., L_n</math> of <math>n</math> distinct elements from <math>GF(2^m)</math> that are not roots of <math>g</math>.

Codewords belong to the kernel of the syndrome function, forming a subspace of <math>\{0,1\}^n</math>: