goedel numbering

suppose we have a function enc that encodes wathever string into a natural number. I am not able to find a surjective function enc:string -> N. I have just found for Goedel Number on wikipedia but the function I was able to find out were not surjective. For having a surjective function we should be able to decide if a string is valid or no. If the string is memeber of a decidable language this is possible, but hotherwise how we can do?
Thanks
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