THE WEIGHT OF THE SYMMETRY CODE FOR p EQUALS 29 AND THE 5-DESIGNS CONTAINED THEREIN.
Abstract
For the practical use of error correcting codes on communications channels, very good, long constructive codes are necessary. The (60, 30) symmetry code over the field of three elements is a long code that has been determined to have the greatest error-correcting properties for a code of length 60 with 30 information symbols over the field of three elements. The (60, 30) symmetry code has more than 10 to the 14th power messages so that determining its weight distribution is a formidable task. In actual use of the code knowledge of the weight distribution is valuable because the weight distribution is required for calculation of the probability of decoding error and failure. In this paper the weight distribution of the (60, 30) symmetry code is given. In connection with this weight distribution, the parameters of some new 5-designs are determined. A conjecture about the entire family of symmetry codes is investigated. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 06, 1970
- Accession Number
- AD0710610
Entities
People
- Vera S. Pless
Organizations
- Air Force Cambridge Research Laboratories