COMBINED FACTORIAL CODING AND ITS PROPERTIES

Abstract

In this paper the authors propose a method of combined factorial data coding directed to the information integrity control that provides a comprehensive protection against intentional alteration of data and communication channel errors. The basic idea of the proposed method consists in combining of procedures of full factorial coding that uses a permutation as a codeword check value, and a cyclic redundancy coding (CRC). In this case a codeword check value of combined factorial code is generated from a codeword check value of full factorial code represented by a polynomial, by the CRC polynomial modulo. The basic properties of the combined factorial code are defined. The assessments of transmission reliability, cryptographic strength and strength against intentional alteration of data are evaluated. A comparative analysis of detecting ability (probability of an error undetected by the code) and energy gain for the full and combined factorial coding is done on the condition of independence of errors that appear in communication channel and their binomial distribution. The ways of improvement of the presented assessment of the probability of an undetected by factorial code error are defined. Recommendations for the use of full and combined factorial coding are given.