Factorial coding with several checksums

The work offers and discusses in detail the methods of factorial coding with several checksums. These methods are used for solving complex problems of data integrity and cryptographic protection, and are aimed at reducing the time of code word formation and the amount of used memory due to parallel processing of data that comes to the encoder and decoder input. The method of systematic factorial coding with several checksums uses a concatenation of several check sequences calculated by different parts of information block as a code word check sequence. Non-systematic factorial coding with several checksums replaces the information sequence with a concatenation of several permutations calculated for different blocks into which a sequence of information symbols is divided. For the proposed coding methods the dependences of undetected error and energy gain probability assessments from the length of encoder input information vector are studied. The comparison of error detecting ability metrics is done for the factorial codes with several checksums and other error detection codes.