A Study of Error-Correcting Codes, I
In his admirably succinct fashion, Russell once defined mathematics as the study of implications and this paper is an example of what he had in mind. The authors, making good on an earlier promise, began a lengthy and detailed investigation of code properties, their characterizations, and implications for a per word model allowing only substitution errors. In this their first report (August 1966), they concentrate on just two properties. Their formal exposition requires the introduction of a variety of new notions, auxiliary results, and technical tools in order to forge the theory. As frequently happens in such activity some of their results can be carried over and applied to one of the fields of pure mathematics, the theory of free semigroups.
KeywordsAdmissibility Mapping Free Semigroup Substitution Error Simple Code Unique Homomorphism
Unable to display preview. Download preview PDF.