  A non-singlet QCD analysis of the structure function $xF_3$ up to NNLO is
performed based on the Bernstein polynomials approach. We use recently
calculated NNLO anomalous dimension coefficients for the moments of the $xF_3$
structure function in $\nu N$ scattering. In the fitting procedure, Bernstein
polynomial method is used to construct experimental moments from the $xF_3$
data of the CCFR collaboration in the region of $x$ which is inaccessible
experimentally. We also consider Bernstein averages to obtain some unknown
parameters which exist in the valence quark densities in a wide range of $x$
and $Q^2$. The results of valence quark distributions up to NNLO are in good
agreement with the available theoretical models. In the analysis we determined
the QCD-scale $\Lambda^ {\bar{MS}}_{QCD, N_{f}=4}=211$ MeV (LO), 259 MeV (NLO)
and 230 MeV (NNLO), corresponding to $\alpha_s(M_Z^2)=0.1291$ LO,
$\alpha_s(M_Z^2)=0.1150$ NLO and $\alpha_s(M_Z^2)=0.1142$ NNLO. We compare our
results for the QCD scale and the $\alpha_s(M_Z^2)$ with those obtained from
deep inelastic scattering processes.
