On the minimum weight of simple full-length array LDPC codes

Simple and full-length array LDPC codes (SFA-LDPC codes) is a class of LDPC codes which are algebraically constructed from a family of array codes. The minimum weight of SFA-LDPC codes has been investigated in literatures, but exact minimum weight of the code is not known except for some small parameters. In this paper it is shown that the class of SFA-LDPC codes which are denoted by
CA
(
p
, 4) in this paper contains a codeword whose minimum weight is 10 or less, if
p
is a prime number greater than 7. Combined with the Yang's lower bound on the minimum weight of
CA
(
p
,4), this implies that the minimum weight of
CA
(
p
, 4) is exactly 10 for any prime p with
p
> 7.