Which coding to choose with the correction of single errors and the detection of others?

Question

Mathematics

I want to store short records (say 32 bits) in NOR flash, I really want to have single error correction and reliable detection of all others. I want to add an integer number of bytes.
what we protect ourselves from:
1. an unlikely bit error;
2. quite probable error "signed garbage" (power off at the time of recording, software failure, whatever).
what comes to mind:
at least 6 bits need to be added to be able to correct a single error - the Hamming code (63, 57).
in total, 2 bits remain in this byte, which is too small for something meaningful. so we add another byte - we get 10 bits, in which it is quite possible to store the CRC.
it turns out that if we have a random set of bits instead of data, then the probability of a CRC match is no more than 0.1% - not so small, of course, but not bad.
Is this normal or bullshit?
I'm confused that both CRC and Hamming Code are based on Hamming Distance, is it reasonable to use them together?

Answer 1

Encode Solomon .
Details: https://habr.com/en/post/191418/