The message decryption step will use the same unique key to perform the reverse circular permutation on the encrypted message and find the correct code words assignment, which will reveal the original message.
It is important to remark that for all partitions within this family we have that (i) the order of the subsets is the same and is given by the reverse order of the permutation ; (ii) the cardinality of the th subset is the same, namely,.
Take the order on the permutations in reverse lexicographic order: i > j if and only if i is less than j as numbers.
In the case of the unique dinucleotide repeats, the most abundantly reported motif was GAn (including complementary, reverse, and reverse-complementary permutations: CT, AG, and TC in descending order of frequency), accounting for approximately 34% of all motifs in the data set and 66% of all dinucleotide repeats.
Repeats with unit patterns being circular permutations and/or reverse complements were considered as one type in this study [ 27, 57].
While recording the count of a particular repeat motif, circular permutations and/or reverse complements of each other were clustered together (e.g. AC = GT = CA = TG, ACG = CGA = GCA = TGC = GCT = CGT = AGC = TCG = CAG = GTC = TGC = GAC and AAC = ACA = CAA = TTG = TGT = GTT) [ 5].
Unmodified Fasta files for each rickettsial genome were used as input, except that the R. sibirica genome sequence was reindexed using the reverse-complement of its circular permutation from the original position 668301.
Unmodified Fasta files for each rickettsial genome were used as input, except that the R. sibirica genome sequence was re-indexed as before [81] using the reverse-complement of its circular permutation from the original position 668301.
The second most abundant dinucleotide motif was CAn (including the reverse, reverse complement, and complementary permutations: AC, GT, and TG) accounting for 15% of all motifs and 30% of all dinucleotide repeats.
This guarantees that every permutation can be reversed within a single step.
