Citation
Abstract
New cyclic group codes of length 2™— 1 over (m — j)-bit symbols are introduced. These codes can be systematically encoded and decoded algebraically. The code rates are very close to Reed-Solomon (RS) codes and are much better than Bose-Chaudhuri-Hocquenghem (BCH) codes (a former alternative). The binary (m — j)tuples are identified with a subgroup of the binary m-tuples which represent the field GF(2™). Encoding is systematic and involves a two-stage procedure consisting of the usual linear feedback register (using the division or check polynomial) and a small table lookup. For low rates, a second shift-register encoding operation may be invoked. Decoding uses the RS error-correcting procedures for the m-tuple alphabet, 1.e., the elements of the field GF(2™). Appendices A and B list (m — j)-tuple codes form = 4, 5, and 6.
Details
- Volume
- 42-108
- Published
- February 15, 1992
- Pages
- 84–95
- File Size
- 459.7 KB