Your ban is valid, i.e. backed by clear evidence of hack usage, and therefore won't be lifted.
If you didn't cheat, then you are probably a victim of cd-key theft and a cheater used your cd-key and got banned with it. If you think that this is the case and you can prove that you are the legitimate owner of the cd-key (via proof of purchase, etc.), please contact the game developers at support@bistudio.com and ask them for help. They might be able to disable your old cd-key and give you a new one, given that there is actual evidence of theft. Note that there is nothing BE can do about others getting access to your system (via cd-key stealers, there is a news post about this issue on battleye.com) and stealing personal data such as your cd-key, that's entirely your own responsibility. Also, it's technically not possible for hackers to steal your cd-key in-game.
Otherwise the only way to get unbanned and be able to play on BE servers again is to buy a new copy or cd-key of the game (ArmA 2: Operation Arrowhead). Please understand that no further details about your ban can be revealed and no further instructions on how to get unbanned can be provided.
Regards,
Bastian Suter
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А пойдём со мной тропинками нежности в страну любви?