The High Court has heard arguments about a Centrelink fraud case that could affect dozens of similar cases around the country.

Adelaide woman Malgorzata Poniatowska pleaded guilty to 17 counts of obtaining a financial advantage from the Commonwealth, knowing she had no entitlement to it.

She had failed to advise Centrelink she was earning an income while still receiving the single parenting payment.

But she appealed her conviction and the Supreme Court of South Australia agreed with her.

The full court found her alleged conduct did not amount to an offence.

Now the Commonwealth has appealed that ruling in the High Court.

It has argued the court was wrong to find an offence cannot be committed by failing to do something.

But Poniatowska's lawyers argued there was no law that says a recipient must inform Centrelink of a change in circumstance.

The High Court has reserved its judgment.