Error Correcting Code and Graph Theory

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I am currently in an introductory graph theory class, and we are supposed to give a short presentation by the end of the semester.

Recently, I've learned (a very small amount) about error correcting codes. Specifically, I looked at one basic example where there is a chooser and an asker. The chooser picks a number, 0-15, and when he is asked questions, he can lie up to 1 time. The asker has 7 questions to determine what the number is and where/if a lie was told.

I have a feeling that such a problem could be solved using a minimum vertex cover of a graph, but Im not sure. My question is if anyone could point me towards an arXiv paper or has any other advice for me.

Thanks in advance!