NCODA isn't available outside the US Navy. However, HYCOM can be used with any 3DVAR or MVOI data assimilation package you have access to providing it assimilates altimeter observations.
NCODA uses synthetic profiles to project SSH anomaly (from altimeters) in the vertical. Most other data assimilation packages use a variant of Cooper-Haines to do this.
HYCOM does not care where the analysis comes from but utilities from HYCOM-tools must be used to pre-process a HYCOM archive file to z-space to be used as the 1st guess to the cycling DA and then to post-process the z-level 3DVAR analysis (or the innovations) back to a hycom snapshot or difference archive in layer space to be incrementally inserted into HYCOM.
We don't currently have an example of this process in HYCOM-examples. Alex is away at present but I'll get her to add an example, which might be from the HYCOM-TSIS reanalysis, or it might be from an isolated eddy test case which we are using to test several DA methods. Note that the example won't include the DA package, only the HYCOM-tools and HYCOM setup to do DA.
Alan.