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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 $f(x)$ is the redundancy part. In contrast to that, a non-separate code word $C$ would be $f_2(x)$ where $f_2$ encodes the word to a redundant representation such as e.g. AN-codes.

So far, I know (multi) residue codes. I found another form of residue codes in http://mark.bu.edu/papers/192.pdf where $f(x) = x^2 \text{ mod } p$ but I haven't found any others. Can someone point me to information to other codes of that type?

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  • $\begingroup$ This is right, but linear codes are not arithmetic codes and not closed under integer addition. $\endgroup$ – Peter W. Feb 22 '17 at 14:07
  • $\begingroup$ We prefer that references fulfill the minimal scholarly requirements and be as robust over time as possible (e.g., include title, author, and where published, so we can still find the paper if the link stops working). Can you take a moment to improve your post in this regard? We have collected some advice here. Thank you! $\endgroup$ – D.W. Feb 28 '17 at 17:18

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