ON BOSE-CHAUDHURI-HOCQUENGHEM CODES OVER GF (Q).
Abstract
Two related aspects of the BCH codes have been investigated. The problems are (1) to have a better knowledge concerning their minimum distances, and (2) to find decoding methods not limited by the BCH bounds. A theory is presented which enables one to determine if a particular BCH code has minimum distance larger than its BCH bound. The derivation of this new theory is based on the Mattson-Solomon approach. The new results are easy to apply as illustrated by several examples. They are applicable to many codes including the well-known Golay (11,6) code over GF(3). A general algebraic full-power decoding method is outlined. In addition, two different methods are presented for the two special cases: (1) the decoding of the two Golay perfect codes to its full error-correcting capability, and (2) the decoding of concactonated codes. All decoding methods are found to be quite practical. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1966
- Accession Number
- AD0636524
Entities
People
- Vincent Lum
Organizations
- University of Illinois Urbana–Champaign