  A general result on the explicit form of the general error locator polynomial
for all cyclic codes is given, along with several results for infinite classes
of cyclic codes with $t=2$ and $t=3$. From these, a theoretically justification
of the sparsity of the general error locator polynomial is obtained for all
cyclic codes with $t\leq 3$ and $n<63$, except for three cases where the
sparsity is proved by a computer check. Moreover, we discuss some consequences
of our results to the understanding of the complexity of bounded-distance
decoding of cyclic codes.
