LAUSR

Dear editor, Nonbinary low-density parity-check (NBLDPC) codes have the ability of approaching capacity when decoded iteratively using a probabilistic decoding algorithm. With the increase of the finite field size q, NBLDPC codes over GF(q) have much better performance under iterative decoding for a constant code length. For q sufficiently large, there is no significant performance improvement while increasing q, moreover the column weights of the parity-check matrices of the best codes tend to 2. As an important class of NBLDPC codes, (2, ρ)-regular NBLDPC codes over GF(q) (q > 64), whose parity-check matrices have row weight ρ and column weight 2, perform well over various channels. This class of NBLDPC codes, so-called NBLDPC cycle codes, has attracted much attention [1–3]. Among these works, all designed codes have good performance. For a given code rate and code length, it is of great interest to study which one of them has the best error performance.