MAX-3LIN-EQN is a problem in Computational complexity theory

Computational complexity theory

Computational complexity theory is a branch of the theory of computation in theoretical computer science and mathematics that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other...

 where the input is a system of linear equations (modulo 2). Each equation contains at most 3 variables. The problem is to find an assignment to the variables that satisfies the maximum number of equations.

This problem is closely related to the MAX-3SAT

MAX-3SAT

MAX-3SAT is a problem in the computational complexity subfield of computer science. It generalises the Boolean satisfiability problem which is a decision problem considered in complexity theory. It is defined as:Given a 3-CNF formula Φ MAX-3SAT is a problem in the computational complexity...

 problem. It is NP-hard

NP-hard

NP-hard , in computational complexity theory, is a class of problems that are, informally, "at least as hard as the hardest problems in NP". A problem H is NP-hard if and only if there is an NP-complete problem L that is polynomial time Turing-reducible to H...

to approximate MAX-3LIN-EQN with ratio (1/2 - δ) for any δ > 0.