In coding theory, Justesen codes form a class of error-correcting codes which are derived from Reed-Solomon codes and have good error-control properties.
Let R be a Reed-Solomon code of length N = 2m − 1, rank K and minimum weight N − K + 1. The symbols of R are elements of F = GF(2m) and the codewords are obtained by taking every polynomial ƒ over F of degree less than K and listing the values of ƒ on the non-zero elements of F in some predetermined order. Let α be a primitive element of F. For a codeword a = (a1, ..., aN) from R, let b be the vector of length 2N over F given by
and let c be the vector of length 2N m obtained from b by expressing each element of F as a binary vector of length m. The Justesen code is the linear code containing all such c.
The parameters of this code are length 2m N, dimension m K and minimum distance at least
The Justesen codes are examples of concatenated codes.
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