On the number of minimum weight codewords of SFA-LDPC codes

The number of minimum weight codewords is an important parameter to measure the potential performance of a linear block code. This paper studies the number of minimum weight codewords of simple and full-length array (SFA) LDPC codes. The notion of a cyclic shift closure is introduced, and it is shown that the set of minimum weight codewords of the code is partitioned by cyclic shift closures of minimum weight codewords. Each cyclic shift closure is generated from a special codeword. With the help of computer experiment, general algebraic forms of the special codewords are determined. As the result, the numbers of minimum weight codewords of several classes of SFA-LDPC codes are clearly expressed by formulas.