Let C$1$ be a $($n$1,$ M$,$ d$1)$ q$-$ary code and C$2$ a $($n$2,$ M$,$ d$2)$ q$-$ary code.

Assume that we have named the codewords:

C$1=\{$w$1,$ w$2,...,$ wM $\},$

C$2=\{$v$1,$ v$2,...,$ vM $\}.$

Define the new code C$3$ as the set of words wivi for i $=1,...,$ M $.$ Find with

justification the parameters n$,$ M$,$ d for the code C$3.($The data may not be enough

to determine the distance d of the new code C$3$ precisely. But you can say that d is

greater than some number. Which number?$)$