  Determining deep holes is an important open problem in decoding Reed-Solomon
codes. It is well known that the received word is trivially a deep hole if the
degree of its Lagrange interpolation polynomial equals the dimension of the
Reed-Solomon code. For the standard Reed-Solomon codes $[p-1, k]_p$ with $p$ a
prime, Cheng and Murray conjectured in 2007 that there is no other deep holes
except the trivial ones. In this paper, we show that this conjecture is not
true. In fact, we find a new class of deep holes for standard Reed-Solomon
codes $[q-1, k]_q$ with $q$ a prime power of $p$. Let $q \geq 4$ and $2 \leq
k\leq q-2$. We show that the received word $u$ is a deep hole if its Lagrange
interpolation polynomial is the sum of monomial of degree $q-2$ and a
polynomial of degree at most $k-1$. So there are at least $2(q-1)q^k$ deep
holes if $k \leq q-3$.
