A proof is presented for the existence of the optimum burst-error-correcting irreducible Goppa codes whose burst-error-correcting capabilities arbitrarily approach the Wyner-Ash bound and Sharma-Dass bound for very large n. On the basis of this result

the asymptote of the burst-error-correcting on these irreducible Goppa codes is discussed. The result is that the most parts of the irreducible Goppa codes over GF（qm） have the burst-correcting capabilities n-k-nε/2≤b≤n-k/2

i. e. there are irreducible Goppa codes over GF （qm）

whoseburst-correcting capabilities are able to approach the Wyner-Ash bound

but the asymptote of the burst-correcting capabilities for these Goppa codes is no good

i. e. b/n may possibly approach zero

when n→∞

and R remains constant.