Sorry, but that's completely off base.

The elements of @biu contain references, so you could do

$biu[$i]->[4]->[$k]
[download]

but -> is optional between indexes, so the following are all fine

$biu[$i]->[4]->[$k]
$biu[$i]->[4][$k]
$biu[$i][4]->[$k]
$biu[$i][4][$k]
[download]

$biu->[$i][4][$k] dereferences the reference in $biu, but there's no such variable in the program.