On Subspace Subcodes Of Reed-Solomon Codes

In this paper, by redescribing Subspace Subcodes of Reed-Solomon Codes,we getsome sufficient and necessary conditions whether a vector is a code of it with thespectrum method. And for some special Subspace Subcodes of Reed-Solomon codes, weget some practical methods to encode them and some simpler formula to compute thedimension of them which do not depend on the computation of the rank ofcyclotomicmatrixes. Finally, some initial results on the minimum Hamming distance of such codesare also given in this paper.