Binding a List of Strings to MVC Controller via form submission

Question

I'd like to allow end users to provide a comma separated string in a text box, and have that string be split on the comma and returned to the controller as a list of strings via a form submission. Here's the code I have so far:

var me = this;

        var $checkNbrInput = $('#checkNumberInput');

        var checkNbrs = $checkNbrInput.val();
        var checkNbrArrayCleansed = checkNbrs.replace(' ','').split(',');

        me._checkNumberArray.push.apply(me._checkNumberArray, checkNbrArrayCleansed);
        var checkNumberArrayObj = [];

        me._checkNumberArray.map(function(val, i) {
            checkNumberArrayObj[i] = { name: 'CheckSearch.CheckNumbers', value: val };
        });
        console.log(checkNumberArrayObj);
        var paramString = $.param(checkNumberArrayObj);
        console.log(paramString);

        $('.check-numbers').val(paramString); //form value 
        $('#checkNumberCount').text(me._checkNumberArray.length);
        $checkNbrInput.val('');

The paramString being assigned to the .check-numbers form field is being built correctly, however its being bound to the first member of the List and not being split up as separate list members.

What I want on the server side for this List:

('42','67','7899') - 3 list members

What I'm getting

('CheckSearch.CheckNumbers=42&CheckSearch.CheckNumbers=67&CheckSearch.CheckNumbers=7899') - 1 list member.