S. Kim et al. have been analyzed the girth of some algebraically structured quasi-cyclic (QC) low-density parity-check (LDPC) codes, i.e. Tanner $(3,5)$ of length $5p$, where $p$ is a prime of the form $15m+1$. In this paper, by extension this method to Tanner $(3,7)$ codes of length $7p$, where $p$ is a prime of the form $21m+ 1$, the girth values of Tanner $(3,7)$ codes will be derived. As an advantage, the rate of Tanner $(3,7)$ codes is about $0.17$ more than the rate of Tanner $(3,5)$ codes.
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Gholami, M., & Mostafaiee, F. (2012). On the girth of Tanner (3,7) quasi-cyclic LDPC codes. Transactions on Combinatorics, 1(2), 1-16. doi: 10.22108/toc.2012.762
MLA
Mohammad Gholami; Fahime Sadat Mostafaiee. "On the girth of Tanner (3,7) quasi-cyclic LDPC codes". Transactions on Combinatorics, 1, 2, 2012, 1-16. doi: 10.22108/toc.2012.762
HARVARD
Gholami, M., Mostafaiee, F. (2012). 'On the girth of Tanner (3,7) quasi-cyclic LDPC codes', Transactions on Combinatorics, 1(2), pp. 1-16. doi: 10.22108/toc.2012.762
VANCOUVER
Gholami, M., Mostafaiee, F. On the girth of Tanner (3,7) quasi-cyclic LDPC codes. Transactions on Combinatorics, 2012; 1(2): 1-16. doi: 10.22108/toc.2012.762
)