Development of an extended text compression nomenclature and its application to the gray codes in the encoding of chromosomes

Abstract

A nomenclature is a naming convention suitable for subsequent study of the properties/characteristics of an object or system. In the context of this paper, the object is a text document or code. Some of the existing standard nomenclatures on codes include Algebraic Coding Theory, Information Theory, the Theory of Error Detection and Correction Codes, and Group Presentation theory. The present paper takes its root from Algebraic Coding Theory and Group Presentation Theory. In it, an extended nomenclature is developed for uniform binary digital text documents/codes. This is based on an earlier ‘code presentation’ nomenclature which was formulated in terms of a lossless binary text compression algorithm. The present paper introduces additional statements of theorems and proofs and this is thereafter applied to the study and discovery of new characteristics of the Gray codes. The significance of the nomenclature is that an entire code (in this case a Gray code), with its exact ordered sequence, can be constructed by merely using its characteristics. The nomenclature was also applied to the encoding of chromosomes in Genetic algorithm/Bioinformatics, thereby reducing the number of storage spaces occupied by the genetic sequences.

Keywords: Nomenclature, Binary text, Code presentation, Chromosomes, Genetic algorithm, Bioinformatics, Gray codes.