# finding the overhead and distance of an unknown code based on message making algorithm

For an information word M with m bits that is coded as following:

1. M Is coded into a word A using an unknown code that allows detection of not more than one error.
2. 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!

• Hi. Please try to format nicer your questions. Uppercase letters exist for a reason. – leonbloy Apr 8 at 1:24
• did it. now could you please help me with my question please? – hps13 Apr 8 at 9:47