codewords
Synonyms
Examples
Although the codewords as produced by the above encoder schemes are not the same, there is a duality between the coefficients of polynomials and their values that would allow the same codeword to be considered as a set of coefficients or a set of values.
Any combination of K codewords received at the other end is enough to reconstruct all of the N codewords.
Formally, the set of codewords of the Reed–Solomon code is defined as follows: : Since any two distinct polynomials of degree less than agree in at most points, this means that any two codewords of the Reed–Solomon code disagree in at least positions.
One requirement for line transmission is that there should be no DC build-up on the line, so the accumulated DC build-up is monitored and the codewords are chosen accordingly.
Practical decoding involved changing the view of codewords to be a sequence of coefficients as explained in the next section.
Reed & Solomon's original view: The codeword as a sequence of values There are different encoding procedures for the Reed–Solomon code, and thus, there are different ways to describe the set of all codewords.