The efficient code construction of regular LDPC codes that can effectively reduce the encoding complexity is still attracting a lot of attention from the research community. This paper presents a code construction method for (3, k) regular LDPC code that utilizes combination of a deterministic part and a partially random part in parity check matrix design. The parity check matrix (H), consisting of parity part (Hp) and information part (H i), is so designed as to have a girth of, at least, 6 and to generate various code rates by maintaining the number of rows in H matrix while only changing the number of columns in the information part (Hi). Our code construction is able to reduce encoding complexity by avoiding any preprocessing step during encoding. © 2008 IEEE.