22 research outputs found
On deep holes of generalized Reed-Solomon codes
Determining deep holes is an important topic in decoding Reed-Solomon codes.
In a previous paper [8], we showed that the received word is a deep hole of
the standard Reed-Solomon codes if its Lagrange interpolation
polynomial is the sum of monomial of degree and a polynomial of degree at
most . In this paper, we extend this result by giving a new class of deep
holes of the generalized Reed-Solomon codes.Comment: 5 page
On the subset sum problem over finite fields
The subset sum problem over finite fields is a well-known {\bf NP}-complete
problem. It arises naturally from decoding generalized Reed-Solomon codes. In
this paper, we study the number of solutions of the subset sum problem from a
mathematical point of view. In several interesting cases, we obtain explicit or
asymptotic formulas for the solution number. As a consequence, we obtain some
results on the decoding problem of Reed-Solomon codes.Comment: 16 page