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I have a stationary gaussian process { X_t } and I have the correlation function p(t) = Corr(X_s, X_(s+t)) = 1 - t/m, where X_t is in {1,2,..,m}, and I want to simulate this process.

The main idea is to write X_t as sum from 1 to N of V_i, X_t+1 as sum from p+1 to N+p V_i and so on, where V_i are uniform variables in [-a, a]. From this point I will use the central limit theorem to prove that X_t is a normal variable. My question is: how can I find the correlation, covariance of X_T and X_t+k for example, a and p using this notification?