ON THE MINIMUM DISTANCE STRUCTURE OF CYCLIC CODES AND DECODING BEYOND THE BCH BOUND,
Abstract
Two related aspects of cyclic codes have been investigated. An attempt has been made to obtain a better understanding concerning their minimum distance, and to find decoding methods to decode beyond the BCH bound. A theory is presented which enables one to obtain better bounds for the minimum distance of a large number of nonprimitive BCH codes. The derivation of this new theory is based on the use of more than one set of consecutive roots of the generator polynomial. The new results are easily applicable since they are based, as the BCH bound, on the pattern of the roots of the generator polynomial. A general decoding method to decode beyond the BCH bound is outlined. In addition a decoding method to decode beyond the BCH bound codes with minimum distance greater than the BCH bound and with multiple sets of consecutive roots is introduced. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1970
- Accession Number
- AD0702901
Entities
People
- Carlos Ricardo Peixoto Hartmann
Organizations
- University of Illinois Urbana–Champaign