On Reed-Solomon codes (Q2430341)

The complexity of decoding the standard Reed-Solomon code is a well-known open problem in coding theory. This two-part paper addresses this problem. In the first part, the author improves known upper bounds for the error distance of a received word to a Reed-Solomon code over \(\text{GF}(q)\). These are useful in determining if efficient list-decoding algorithms can be applied. In the second part, the author proves estimates, and even explicit formulas, for the dimension of trace Reed-Solomon codes in some cases.