use constant NCOLS => 3954;

my $file = $matrixPath.'/'.$info{$transcriptName}{'PATH'};
my $fileSize = -s $file;
die 'Bad filesize' unless $filesize % NCOLS == 0;

open IN, $file or die "Can't open inputfile $file $!";
binmode(IN);
## Note: You're reading the whole file in a single read NO NEED FOR A LOOP.
sysread(IN, my $buffer, $fileSize) or die.
close IN;

## The first (rightmost) unpack splits the buffer into NCOLS length sections of bytes.
## The second unpack breaks each of those into its individual (uchar) integers 
## and puts them in an anonymous array. 
## the map assigns al the anonymous arrays to @matrix.

# Update: template corrected, see posts below.
my @matrix = map[ unpack 'C*', $_ ], unpack '(a' . NCOLS . ')*', $buffer;
...