  We present an analysis of the $xF_3(x,Q^2)$ structure function and
Gross-Llewellyn Smith(GLS) sum rule taking into account the nuclear effects and
higher twist correction. This analysis is based on the results presented in "N.
M. Nath et al., Indian J Phys 90(1), 117 (2016)". The corrections due to
nuclear effects predicted in several earlier analysis are incorporated to our
results of $xF_3(x,Q^2)$ structure function and GLS sum rule for free nucleon,
corrected upto next-next-to-leading order (NNLO) perturbative order and
calculate the nuclear structure function as well as sum rule for nuclei. In
addition, by means of a simple model we have extracted the higher twist
contributions to the non-singlet structure function $xF_3(x,Q^2)$ and GLS sum
rule in NNLO perturbative orders and then incorporated them to our results. Our
NNLO results along with nuclear effect and higher twist corrections are
observed to be compatible with corresponding experimental data and other
phenomenological analysis.
