Is my repentance accepted after I committed adultery, and how is it accepted along with the carrying out of the [prescribed] punishment?

You have committed a heinous major sin, and it is obligatory upon you to repent sincerely, regret the sin, and resolve never to return to it. Allah accepts repentance and makes you like one who has not sinned. Conceal your sin and do not tell anyone about it. The imposition of the prescribed punishment (حد) is not a condition for the validity of repentance. Distance yourself from friends who were the cause of your sin, and replace them with righteous friends who will help you obey Allah, in compliance with the Prophet's (peace be upon him) advice: "Do not associate except with a believer."