On the error distance of extended Reed-Solomon codes
YuJuan Li, Guizhen Zhu · Advances in Mathematics of Communications · 2016
It is well known that the main problem of decoding the extended Reed-Solomon codes is computing the error distance of a word. Using some algebraic constructions, we are able to determine the error distance of words whose degrees are $k+1$ and $k+2$ to the extended Reed-Solomon codes. As a corollary, we can simply get the results of Zhang-Fu-Liao on the deep hole problem of Reed-Solomon codes.