The word "complete" is an adjective and as an adjective it describes the condition of a noun, for example: The updates contain all the necessary information, therefore the updates are complete. The word "completed" is the verb and as a verb it means "finished/perfected", for example: The updates are complete and there is nothing more to do, therefore the updates have been completed. It's important to note that the sentence includes the phrase "by next Friday".So, the answer needs a verb to tell when the updates will be completed, for example "be completed by a certain date or time. So, the answer is "... can be completed." BTW, I think a lot of native English speakers would have trouble answering this question, because the adjective and the verb are very similar, but they are also a little different.

In this case "complete" would not be grammatically correct. In spoken English, it would be acceptable and most people wouldn't think twice about it. However, if you want a grammatically correct sentence, you would have to use "completed." Your sentence is in passive voice so you must use the linking verb "to be" + "past participle." Examples (Passive Voice, Future Tense): A computer will be purchased. My homework can be finished on time. The thief may be punished. If you want to use "complete," you would have to change the sentence to active voice. i.e. If you could complete all the updates by Friday, that would be great. Let me know if you have any questions! ^^

"Completed" would be the better answer, however, if you used "complete", the statement would still be correct, it just wouldn't sound as good to an English speaker.