**Disable All Update Notifications with Code**

    function remove_core_updates(){
            global $wp_version;return(object) array('last_checked'=> time(),'version_checked'=> $wp_version,);
        }
        add_filter('pre_site_transient_update_core','remove_core_updates');
        add_filter('pre_site_transient_update_plugins','remove_core_updates');
        add_filter('pre_site_transient_update_themes','remove_core_updates');

Code will disable update notifications for the WordPress core, plugins, and themes.