an:06221897
Zbl 1302.94071
Frolov, A. A.; Zyablov, V. V.
Bounds on the minimum code distance for nonbinary codes based on bipartite graphs
EN
Probl. Inf. Transm. 47, No. 4, 327-341 (2011); translation from Probl. Peredachi Inf. 47, No. 4, 27-42 (2011).
00296040
2011
j
94B60 94B65
Summary: The minimum distance of codes on bipartite graphs (BG codes) over \(\mathrm{GF}(q)\) is studied. A new upper bound on the minimum distance of BG codes is derived. The bound is shown to lie below the Gilbert-Varshamov bound when \(q\geq 32\). Since the codes based on bipartite expander graphs (BEG codes) are a special case of BG codes and the resulting bound is valid for any BG code, it is also valid for BEG codes. Thus, nonbinary \((q\geq 32)\) BG codes are worse than the best known linear codes. This is the key result of the work. We also obtain a lower bound on the minimum distance of BG codes with a Reed-Solomon constituent code and a lower bound on the minimum distance of low-density parity-check (LDPC) codes with a Reed-Solomon constituent code. The bound for LDPC codes is very close to the Gilbert-Varshamov bound and lies above the upper bound for BG codes.