ON LINEAR PRODUCT CODES AND THEIR DUALS,
Abstract
The value of studying the tensor product of linear codes is demonstrated. The pertinent problems concerning these product codes are outlined. Algebraic techniques for determining the null space of a tensor product space are developed. The understanding of the null space of a product space is useful not only in the development of this report, but also for future research work. Decomposition of the procedure and implementation of encoding and decoding of a product code into those of its component codes are shown. In the case where the component codes are cyclic, the product code has the special feature that its encoder and syndrome calculator can be easily converted to those of its dual codes by programmed switching. A simple decoding scheme; namely, permutation decoding, which is capable of correcting a large fraction of all the correctable errors of a systematic cyclic code, is investigated. It is suggested that it be used either as a part of the correction-detection scheme or in combination with an auxiliary scheme to attain full error correction capability. Finally, the minimum distances of product codes, and suitable communication channels for employing such codes, are discussed. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1966
- Accession Number
- AD0640398
Entities
People
- Lih-jyh Weng
Organizations
- Northeastern University