How about:

chomp( my @lines = <$infile> );
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Or...

use File::Slurp;
my @lines = read_file( $infile, chomp => 1 );
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There's more than one way to do it. Assuming the file doesn't grow to swamp available memory, they all work. I'd say that the File::Slurp method, and the "chomp( my @lines..." method are probably the easiest to look at and immediately know what's happening.

Any method that ends up slurping the file into an array will make $line_count useless after the slurp is done, since you can always say: my $line_count = scalar @lines;

Update: I just noticed that your map method has a couple of bugs (which is one compelling reason to keep it as simple as possible). This:

my @lines = map { chomp; $_; $line_count++; } <$infile>;
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... chomps $_, then referrs to $_ for no reason, then increments $line_count, then pushes each line's line_count onto @lines. In the end, @lines will contain "( 0, 1, 2, 3, 4, 5, ... )". You probably meant to write it like this:

my @lines = map { chomp; $_ } <$infile>;
my $line_count = scalar @lines;
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