On the non-existence for quantum LDPC codes of type IEEE802.16e with rates 1/2 and 2/3B

In this paper, we discuss a construction of CSS codes derived from pairs of practical irregular LDPC codes. Our design of irregular LDPC codes is based the design written in the standardization of IEEE802.16e. Our research has tried to make a CSS code with a pair of LDPC codes of type IEEE802.16e. To our regret, we proved that it was impossible to construct a CSS code if one of classical codes was of type IEEE802.16e with rate 1/2 and 2/3B. We would like to report the discussion on its impossibility in this paper. This is the first paper to analyze the possibility of a CSS code construction by using two irregular LDPC codes which are practically useful.