Get element by part of Name or ID

Your best bet is probably document.querySelectorAll, which you can use any CSS selector with, including an "attribute starts with" selector like input[id^="id_qtedje_"]. It's supported on all modern browsers, and also IE8:

var elements = document.querySelectorAll('input[id^="id_qtedje_"]');

If you wanted just the first match (rather than a list), you could use document.querySelector instead. It returns a reference to the first match in document order, or null if nothing matched.

Alternately, you could give the elements a class name, then use document.getElementsByClassName, but note that while getElementsByClassName was supported in old versions of Chrome and Firefox, IE8 doesn't have it, so it's not as well-supported as the more-useful querySelectorAll in the modern era.

var elements = document.getElementsByClassName("theClassName");

If you use any libraries (jQuery, MooTools, Closure, Prototype, etc.), they're likely to have a function you can use to look up elements by just about any CSS selector, filling the gaps in browser support with their own code. For instance, in jQuery, it's the $ (jQuery) function; in MooTools and Prototype, it's $$.

You can use the starts with selector in jQuery

var listOfElements = $('[name^="id_qtedje_"]')

You may also be interested with the contains and ends with selectors

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Using querySelectorAll, you can do

document.querySelectorAll('[name^="id_qtedje_"]')

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Alternatively:

Assuming that all elements are inputs, you may use this:

function getElementByNameStart(str) {
    var x=document.getElementsByTagName('input')
    for(var i=0;i<x.length;i++) {
        if(x[i].indexOf(str)==0) {
            return x[i];
        }
    }
}

which can be called as getElementByNameStart("id_qtedje_")

Note that this only returns the first element of this type. To return all:

function getElementByNameStart(str) {
    var x=document.getElementsByTagName('input')
    var a=[];
    for(var i=0;i<x.length;i++) {
        if(x[i].indexOf(str)==0) {
            a.push(x[i])
        }
    }
    return a;
}

If the elements are of any type, replace "input" with "*" (beware, this may make your code slow)