Yes, if the message is only 40 bits long there is a 100% chance. But the point is that you still only need 20 bits even if the message is 100000 bits long Beca

Yes, if the message is only 40 bits long there is a 100% chance. But the point is that you still only need 20 bits even if the message is 100000 bits long Because if 50% of bits are corrupted, each bit has a >50% chance of being corrupted, so With 20 bits you have only a 1 in 2^20 chance of missing all the corrupted bits. The 20 bits don't allow you do correct anything, BTW. To do that you need a locally decodable code. What we are talking about here is the ability to detect corruption of the original data.