Error-Correcting Codes,
Abstract
The minimum distances are determined for all quadratic-residue codes of lengths 3, 5, 7, and 11 by means of permutation groups. Upper bounds on the minimum distance are obtained for many lengths up to 50,000 for various ground fields; the method used is cyclotomy. Relations between the (24, 12) Golay code and the (8, 4) extended Hamming code are found by means of a contraction map, which is then applied to find useful relation between the extended (60, 30) quadratic residue code over GF(3) and the (12, 6) Golay code. A theorem reducing the number of vectors to be examined allows a feasible computer determination of the minimum distance of the (60, 30) code. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 31, 1971
- Accession Number
- AD0736461
Entities
People
- Edward F. Assmus Jr.
- Harold F. Mattson Jr.