LDPC codes from the Hermitian curve. (English) Zbl 1125.51005
Summary: In this paper, we study the code \(\mathbb C\) which has as parity check matrix \(\mathbb H\) the incidence matrix of the design of the Hermitian curve and its \((q+1)\)-secants. This code is known to have good performance with an iterative decoding algorithm, as shown by S. J. Johnson and S. R. Weller in [High-rate LDPC codes from unital desings. Proc. ICEE Globecom Conference, San Francisco, CA, 1–5 December (2003)]. We prove that \(\mathbb C\) has a double cyclic structure and that by shortening in a suitable way \(\mathbb H\) it is possible to obtain new codes which have higher code-rate. We also present a simple way to constructing the matrix \(\mathbb H\) via a geometric approach.
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