We present our new measurement of the cross-section for charm dimuon production in neutrino iron interactions based upon the full statistics collected by the NOMAD experiment. After background subtraction we observe 15 344 charm dimuon events, providing the largest sample currently available. The analysis exploits the large inclusive charged current sample ¿ about 9 x 10(6) events after all analysis cuts ¿ and the high resolution NOMAD detector to constrain the total systematic uncertainty on the ratio of charm dimuon to inclusive Charged Current (CC) cross-sections to similar to 2%. We also perform a fit to the NOMAD data to extract the charm production parameters and the strange quark sea content of the nucleon within the NLO QCD approximation. We obtain a value of m(c)(m(c)) = 1.159 +/- 0.075 GeV/c(2) for the running mass of the charm quark in the (MS) over bar scheme and a strange quark sea suppression factor of kappa(s) = 0.591 +/- 0.019 at Q(2) = 20 GeV2/c(2).