  Motivated by an extremal problem on graph-codes that links coding theory and
graph theory, Alon recently proposed a question aiming to find the smallest
number $t$ such that there is an edge coloring of $K_{n}$ by $t$ colors with no
copy of given graph $H$ in which every color appears an even number of times.
When $H=K_{4}$, the question of whether $n^{o(1)}$ colors are enough, was
initially emphasized by Alon. Through modifications to the coloring functions
originally designed by Mubayi, and Conlon, Fox, Lee and Sudakov, the question
of $K_{4}$ has already been addressed. Expanding on this line of inquiry, we
further study this new variant of the generalized Ramsey problem and provide a
conclusively affirmative answer to Alon's question concerning $K_{5}$.
