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A general theory of codes, II: Paradigms and homomorphisms

  • G. R. Blakley
  • I. Borosh
Special Lecture
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1396)

Abstract

When two competing paradigms bear on a single area of study, investigators have more choices at their disposal. This is not always an advantage.

This paper, like its predecessor, adopts a paradigm for codes. This paradigm ignores the purposes which might have given rise to a code, the size of the code, or the arithmetic used in implementing the code. It concentrates solely on the (set-theoretic) structure of that code. Once adopted, this structure-oriented paradigm leads naturally to a theory of homomorphisms for the general theory of codes. Code homomorphisms satisfy the standard isomorphism theorems, respect certain important properties of codes, are compatible with products and quotients, and possess other desirable features. Thus, codes fit into general algebra alongside such familiar objects as groups, graphs and posets.

Keywords

Equivalence Relation General Algebra Dominant Paradigm Isomorphism Theorem Relation Isomorphism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • G. R. Blakley
    • 1
  • I. Borosh
    • 1
  1. 1.Texas A&M UniversityCollege StationUSA

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