What did the decemberists hope to achieve through their uprising?

The officers were driven to revolt by many forces. To begin, they felt that Nicholas did not deserve the throne. Nicholas's older brother, Constantine, stood to inherit the throne first, but when Constantine chose to marry a Polish girl with no royal blood, he relinquished his claim to the throne. In addition, when the previous tsar, Alexander I, wrote out his succession, it was not made public. Instead it was hidden and only brought forth after his death. There was confusion over whether the document was legally binding, and the rebels felt that Nicholas cheated Constantine out of the throne. 
Also, the rebels were active in the new liberal movement from Europe. They wanted a free Russian state, with a federal government and constitution, instead of government under the tsar. However, Nicholas was not known to favor these ideas, and was also less popular with the public than his brother. These combined to give the liberals hope that their time to move had come.