Citation
Abstract
In order to obtain performance superior to that of the (32,6) first-order ReedMuller Code used on Mariner Mars 1969 and 1971 spacecraft, bandwidth limitations make it necessary to consider Reed-Muller codes of higher orders. In this paper, we investigate the weights which can actually occur in the third-order Reed-Muller codes of lengths 256 and 512. For length 256, we succeed in finding the exact set of integers which occur as weights. For length 512, we do the same, except that we cannot decide whether 140 and 372 occur as weights or not. We show, however, that there are no words of weight 132 or 380, a result which adumbrates an important new theorem on Reed-Muller codes. TueroreM | (Ref. 1). The minimum distance d in RM (1;2™) is 27-7,
Details
- Volume
- IV
- Published
- August 15, 1971
- Pages
- 86–94
- File Size
- 786.8 KB