We prove a general form of bit flip formula for the quantum Fourier transform on finite abelian groups and use it to encode some general CSS codes on these groups.

This article aims at analyzing and estimating the function of private consumption and it's long-run relation using error correction model in Iran's economy. To avoid spurious regression we proceeded first by exploring the long-run co-integrating private mechanism to estimate the short-run equation. Since there may be a weakness associated with the Engle-Granger method of co-integration testing, we investigated the cointegration relationship by using Johansen co-integration test. We found strong evidence from the Johansen test that the related variables are integrated. The empirical evidence suggests that the tendency toward consumption is 83% and the speed of adjustment for the long-run private consumption is around 73% implying that about 73 percent of differences between the short-run and long-run consumption level will be adjusted within one year.