For an information word M with m bits that is coded as following:
- M Is coded into a word A using an unknown code that allows detection of not more than one error.
- The code word is the word obtained by a concatenation of A to itself. So A becomes AA and etc..
1)Is it possible to know the overhead in the given code?
2)Is it possible to know the distance of the code?
My attempt:
Since the code allows detection of not more than one error, i assume i am tasked to use hamming code and its properties(allows to fix until 1 bit and detect 2 bits of error if i am not mistaken). So for the questions:
1)In hamming code we don't have to know the code to fix an error in a bit so if the original message length was m bits and we need additional r bits to fix it, Then we obtain $m+r+1=2^r$ , Based on the lower limit: $(m+r+1)∗2^m≤2^{m+r}$
, So it is possible to calculate the overhead.
2)Since hamming distance is the minimal amount of changes in one string to obtain the second, And since the code word is obtained by a concatenation of A to itself, Then the hamming distance should be 2A? or is there information missing that doesn't allow me to fully calculate it?
Would really appreciate your input. Thank you very much!