How to deal with many input fields with the same name, and post to PHP?

Let's say that I have an HTML structure that looks like this. Each left-context-field and right-context-field are related and in the backend it should be possible to link left to its right colleague.

<table>
  <tbody>
    <tr>
      <td>
        <input type="text" class="left-context-field" value="First left value">
      </td>
      <td>
        <input type="text" class="right-context-field" value="First right value">
      </td>
    </tr>
    <tr>
      <td>
        <input type="text" class="left-context-field" value="Second left value">
      </td>
      <td>
        <input type="text" class="right-context-field" value="Second right value">
      </td>
    </tr>
    <tr>
      <td>
        <input type="text" class="left-context-field" value="Third left value">
      </td>
      <td>
        <input type="text" class="right-context-field" value="Third right value">
      </td>
    </tr>
    <tr>
      <td>
        <input type="text" class="left-context-field" value="Fourth left value">
      </td>
      <td>
        <input type="text" class="right-context-field" value="Fourth right value">
      </td>
    </tr>
  </tbody>
</table>

and a user can add as many additional rows as they please. How would I go about posting the values to a PHP file?

Should I wrap all rows in one single huge form, and then call .serializeArray()? Or one form per row?

From a data-oriented approach, what's the best way to deal with this? I'll be sending the data to the back-end, but I want to make the data ass easily accessible for the the backend developer as possible.

Solution

I've Edited meda's Answer, but he is not approving that Edit, So I'm posting it here again.

In HTML forms the way you send arrays is using brackets.

For example

name="values[]"

like this.

<form name = 'vals_form' action = 'php_page.php' method = 'post'>
  <table>
    ... <!-- Your all code -->
    <tr>
      <td>
        <input type="text" class="left-context-field" value="First left value" name="values[]">
      </td>
      <td>
        <input type="text" class="right-context-field" value="First right value" name="values[]">
      </td>
    </tr>
    ...
    <input type = 'submit' value = 'Post Values' />  
  </table>
</form> <!--and close the form tag-->

In PHP you get the array back

$values = $_POST['values'];