There are several ways to force Perl use less memory.

1. using Inline::C create C's subroutine that implements your two-dimensional array
2. use one single scalar value and simulate your array by taking proper substr
3. If your array is really all 1-s with few exceptions, just store such exceptions in another array and write a simple sub that simulates your 2D array.

May be some more.

Courage, the Cowardly Dog