# Error detection code supporting arithmetic

I am looking for error detection codes, which support addition in the encoded domain and are separate (a tuple of ($N$, $R(N)$), where $N$ denotes the functional value and $R(N)$ its redundancy).

So far I know residue codes where $R(N)$ equals $N \text{ mod } p$ and $p$ is a chosen constant. This scheme is closed under addition. Addition is performed by adding the functional part and the redundancy part mod $p$.

Can someone point me to other resources that describe coding schemes that are separate and support addition?

Thank's for the comments. Let me clarify my question. I want to have addition modulo $n$ where $n = 2^q$ with $q > 1$, e.g. $q = 32$, to support 32-bit integer addition.

Linear codes support a bitwise addition modulo 2, which is not suitable for my case.

• By "Support addition" do you mean linear codes? – Ariel Oct 4 '17 at 10:45
• Any code that is linear mod n will suffice. – D.W. Oct 11 '17 at 14:13