Combined Factorial Coding and Its Properties

In this paper the authors propose a method of combined factorial data coding directed to the information integrity control that providesa comprehensive protection against intentional alteration of data and communication channel errors. The basic idea of the proposed methodconsists 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 coderepresented by a polynomial, by the CRC polynomial modulo. The basic properties of the combined factorial code are defined. The assessmentsof transmission reliability, cryptographic strength and strength against intentional alteration of data are evaluated. A comparative analysis ofdetecting ability (probability of an error undetected by the code) and energy gain for the full and combined factorial coding is done on thecondition of independence of errors that appear in communication channel and their binomial distribution. The ways of improvement of thepresented 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.