Usain Bolt was "not pleased" to be forced into handing over his 2008 Olympic 4x100 metre relay gold medal, but did state he would help finance an appeal if necessary.
His was one of 454 selected doping samples retested by the International Olympic Committee (IOC) a year ago, and has been found to contain the banned stimulant methylhexaneamine.
Stuart Stimpson, Carter's legal adviser said that his client would embed petition with the Court of Arbitration for Sports (CAS).
"Things happen in life, if it's confirmed or whatever and I need to give back my gold medal it's not a problem to me".
Bolt completed an unprecedented "triple triple" at last summer's Rio Olympics, winning gold in each of the 100m, 200m and 4x100m events for the third time.
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It maintains diplomatic relations with over 100 states and the European Union and permanent observer status at the United Nations. Boeselager says Festing offered no valid reason for him to resign, and that he was therefore under no obligation to obey.
Carter tested positive after it was revealed that he had traces of a stimulant that has been banned called Methylhexanamine.
Trinidad and Tobago are set to be promoted to gold in the Beijing 4x100, in which Jamaica set a then world record, with Japan moving up to silver and Brazil earning bronze.
The latest International Olympic Committee ruling also covered Russian triple-jump athlete Tatiana Lebedeva, who was retroactively disqualified from the Beijing Games, where she won a silver medal, after reanalysis of samples resulted in a positive test for the prohibited substance dehydrochlormethyltestosterone (turinabol)..
Carter "is found to have committed an anti-doping rule violation pursuant to the IOC Anti-Doping Rules applicable to the Games of the XXIX Olympiad in Beijing in 2008". The global athletics' federation (IAAF) is responsible for modifying race results and sanctioning athletes.
Bolt is one of four members of Jamaica's relay team who will have to return their medals after one of them tested postive for a performance-enhancing drug.
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