# Questions tagged [error-correcting-codes]

Error correcting codes are used to transmit information through a noisy channel. They also have applications in theoretical computer science and combinatorics. Some well known error correcting codes are Hamming codes, Reed–Solomon codes, and Reed–Muller codes.

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### minimal distance of a self correcting code

i wonder: how can i find minimal distance of a self correcting code in following situation: if we know that a code can fix every 3 errors(if not more than 3 errors, the word is recovered) and can ...
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### Separate arithmetic codes closed under addition

For error detection purpose I am looking for separate arithmetic codes which are closed under integer addition. By separate, I mean the code word $C$ for message $x$ is a tuple $(x,f(x))$ where $f(x)$...
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### Protecting data unequally using Error Correction Codes

Say I'd like to transmit a 100-bit packet which has a field containing a continuous value. I'd like to protect this value with an error correction code but an error in the MSB of this value is much ...
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### CRC error detection

I know that to find an error in signal we have to divide given signal with given polynomial and if 0 remains there is no error. But if I have received signal: 0000 0101 0101 0000 1010 0101 and ...
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### Does there exist a Reed-Solomon-like code over decimal symbols?

A Reed-Solomon error-correcting code consisting of N symbols is guaranteed to detect up to N single-symbol replacements in an arbitrarily long input plus the ECC itself, and is also guaranteed to ...
Let's say you have $n$ symbols. You can encode a $\log_2(n!)$-bit message by permutating the symbols. I will call this a permutation code (if you have seen this concept before, I would love to see a ...
I have to solve this exercise in information theory: A binary not symmetrical channel has probability of transition from 0 to 1 $P(output=1|input=0)=p$ and probability of transition from 1 to 0 \$P(...