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.
be a Reed-Solomon code of length N
− 1, rank K
and minimum weight N
+ 1. The symbols of R
are elements of F
) 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
. For a codeword a
, ..., aN
) from R
, let b
be the vector of length 2N
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.
- J. Justesen (1972). "A class of constructive asymptotically good algebraic codes". IEEE Trans. Info. Theory 18 652–656.
- F.J. MacWilliams; N.J.A. Sloane The Theory of Error-Correcting Codes. North-Holland.