1. A decoding device for an absolute positioning code, comprising: a linear feedback shift register, comprising n registers, wherein the n registers load the absolute positioning code with a first frequency, and the linear feedback shift register performs shifting operation according to a clock signal having a second frequency greater than or equal to the first frequency; a lookup table circuit, configured to output a lookup result and a valid flag according to values stored in the n registers, wherein the lookup result has k different data, k≦(2 n −1), and the valid flag indicates whether the lookup result is valid; a counter circuit, configured to reset according to the valid flag, and to perform counting operation according to the clock signal to generate a counting result; and a computation circuit, configured to perform calculation according to the lookup result and the counting result to generate a decoding result when the valid flag indicates valid.