  Given a constraint satisfaction problem (CSP) on $n$ variables, $x_1, x_2,
\dots, x_n \in \{\pm 1\}$, and $m$ constraints, a global cardinality constraint
has the form of $\sum_{i = 1}^{n} x_i = (1-2p)n$, where $p \in (\Omega(1), 1 -
\Omega(1))$ and $pn$ is an integer. Let $AVG$ be the expected number of
constraints satisfied by randomly choosing an assignment to $x_1, x_2, \dots,
x_n$, complying with the global cardinality constraint. The CSP above average
with the global cardinality constraint problem asks whether there is an
assignment (complying with the cardinality constraint) that satisfies more than
$(AVG+t)$ constraints, where $t$ is an input parameter.
  In this paper, we present an algorithm that finds a valid assignment
satisfying more than $(AVG+t)$ constraints (if there exists one) in time
$(2^{O(t^2)} + n^{O(d)})$. Therefore, the CSP above average with the global
cardinality constraint problem is fixed-parameter tractable.
