Citation
Abstract
A self-dual code of length 48, dimension 24, with Hamming distance essentially equal to 12 is constructed here. There are only six codewords of weight 8. All the other codewords have weights that are multiples of 4 and have a minimum weight equal to 12. This code may be encoded systematically and arises from a strict binary representation of the (8,4;5) Reed-Solomon (RS) Code over GF (64). The code may be considered as six interrelated (8,7;2) codes. The Mattson—Solomon representation of the cyclic decomposition of these codes and their parity sums are used to detect an odd number of errors in any of the six codes. These may then be used in a correction algorithm for hard or soft decision decoding. A (72,36;15) box code was constructed from a (63,35;8) cyclic code. The theoretical justification is presented herein. A second (72,36;15) code is constructed from an inner (63,27;16) Bose-Chaudhuri-Hocquenghem (BCH) code and expanded to length 72 using box code algorithms for extension. This code was simulated and verified to have a minimum distance of 15 with even weight words congruent to 0 modulo 4. The decoding for hard and soft decision is still more complex than the first code constructed above. Finally, an (8,4;5) RS Code over GF(512) in the binary representation of the (72,36;15) box code gives rise to a (72,36;16*) code with nine words of weight 8, and all the rest have weights > 16.
Details
- Volume
- 42-115
- Published
- November 15, 1993
- Pages
- 105–109
- File Size
- 304.0 KB