Strong Trinucleotide Circular Codes

Table 3

The prefixes and suffixes of the pattern of the 28 classes of 𝐿𝐷𝐿-strong 20-trinucleotide circular codes (Tables 2(a)–2(c)). For each pattern 𝑋, the subset 𝐿₁ (resp. 𝐿₃) of {𝑎,𝑏,𝑐,𝑑} consists of the letters 𝑙₁ (resp. 𝑙₃) that appear at least once in prefix (resp. suffix) position of the trinucleotides of 𝑋. Similarly, the subset 𝐷₁ (resp. 𝐷₂) of {𝑎,𝑏,𝑐,𝑑}² consists of the diletters 𝑑₁ (resp. 𝑑₂) that appear at least once in prefix (resp. suffix) position of the trinucleotides of 𝑋.

Codes	𝐿1	𝐿3	𝐷1	𝐷2
𝐶1	𝑎,𝑏,𝑐,𝑑	𝑎,𝑏,𝑐,𝑑	𝑎𝑎,𝑏𝑎,𝑏𝑏,𝑏𝑑,𝑐𝑎,𝑐𝑐,𝑐𝑑,𝑑𝑑	𝑎𝑏,𝑎𝑐,𝑎𝑑,𝑏𝑐,𝑐𝑏,𝑑𝑎,𝑑𝑏,𝑑𝑐
𝐶2	𝑎,𝑏,𝑐,𝑑	𝑎,𝑏,𝑐,𝑑	𝑎𝑎,𝑏𝑎,𝑏𝑐,𝑏𝑑,𝑐𝑐,𝑑𝑎,𝑑𝑏,𝑑𝑐	𝑎𝑏,𝑎𝑐,𝑎𝑑,𝑏𝑏,𝑐𝑎,𝑐𝑏,𝑐𝑑,𝑑𝑑
𝐶3	𝑎,𝑏,𝑐,𝑑	𝑎,𝑏,𝑐,𝑑	𝑎𝑎,𝑎𝑐,𝑎𝑑,𝑏𝑏,𝑏𝑐,𝑏𝑑,𝑐𝑑,𝑑𝑐	𝑎𝑏,𝑏𝑎,𝑐𝑎,𝑐𝑏,𝑐𝑐,𝑑𝑎,𝑑𝑏,𝑑𝑑
𝐶4	𝑎,𝑏,𝑐,𝑑	𝑎,𝑏,𝑐,𝑑	𝑎𝑏,𝑎𝑐,𝑎𝑑,𝑏𝑑,𝑐𝑎,𝑐𝑏,𝑐𝑑,𝑑𝑏	𝑎𝑎,𝑏𝑎,𝑏𝑏,𝑏𝑐,𝑐𝑐,𝑑𝑎,𝑑𝑐,𝑑𝑑
𝐶5	𝑎,𝑏,𝑐,𝑑	𝑏,𝑐,𝑑	𝑎𝑎,𝑏𝑎,𝑏𝑏,𝑐𝑎,𝑐𝑏,𝑐𝑐,𝑑𝑎,𝑑𝑏,𝑑𝑑	𝑎𝑏,𝑎𝑐,𝑎𝑑,𝑏𝑐,𝑏𝑑,𝑐𝑑,𝑑𝑐
𝐶6	𝑎,𝑏,𝑐,𝑑	𝑏,𝑐,𝑑	𝑎𝑎,𝑏𝑎,𝑏𝑏,𝑐𝑎,𝑐𝑏,𝑐𝑑,𝑑𝑎,𝑑𝑑	𝑎𝑏,𝑎𝑐,𝑎𝑑,𝑏𝑐,𝑏𝑑,𝑑𝑏,𝑑𝑐
𝐶7	𝑎,𝑏,𝑐,𝑑	𝑏,𝑐,𝑑	𝑎𝑎,𝑏𝑎,𝑏𝑏,𝑐𝑎,𝑐𝑏,𝑐𝑑,𝑑𝑎,𝑑𝑏,𝑑𝑐	𝑎𝑏,𝑎𝑐,𝑎𝑑,𝑏𝑐,𝑏𝑑,𝑐𝑐,𝑑𝑑
𝐶8	𝑎,𝑏,𝑐,𝑑	𝑎,𝑏,𝑐,𝑑	𝑎𝑎,𝑏𝑎,𝑏𝑏,𝑏𝑑,𝑐𝑎,𝑐𝑏,𝑐𝑑,𝑑𝑑	𝑎𝑏,𝑎𝑐,𝑎𝑑,𝑏𝑐,𝑑𝑎,𝑑𝑏,𝑑𝑐
𝐶9	𝑎,𝑏,𝑐,𝑑	𝑏,𝑐,𝑑	𝑎𝑎,𝑏𝑎,𝑏𝑏,𝑏𝑑,𝑐𝑎,𝑐𝑐,𝑐𝑑,𝑑𝑎	𝑎𝑏,𝑎𝑐,𝑎𝑑,𝑏𝑐,𝑐𝑏,𝑑𝑏,𝑑𝑐,𝑑𝑑
𝐶10	𝑎,𝑏,𝑐,𝑑	𝑎,𝑏,𝑐,𝑑	𝑎𝑎,𝑏𝑎,𝑏𝑐,𝑏𝑑,𝑐𝑐,𝑑𝑎,𝑑𝑐	𝑎𝑏,𝑎𝑐,𝑎𝑑,𝑐𝑎,𝑐𝑏,𝑐𝑑,𝑑𝑏,𝑑𝑑
𝐶11	𝑎,𝑏,𝑐,𝑑	𝑏,𝑐,𝑑	𝑎𝑎,𝑏𝑎,𝑏𝑐,𝑏𝑑,𝑐𝑎,𝑑𝑎,𝑑𝑏,𝑑𝑐	𝑎𝑏,𝑎𝑐,𝑎𝑑,𝑏𝑏,𝑐𝑏,𝑐𝑐,𝑐𝑑,𝑑𝑑
𝐶12	𝑎,𝑏,𝑐,𝑑	𝑏,𝑐,𝑑	𝑎𝑎,𝑏𝑎,𝑏𝑐,𝑏𝑑,𝑐𝑎,𝑐𝑑,𝑑𝑎,𝑑𝑐	𝑎𝑏,𝑎𝑐,𝑎𝑑,𝑐𝑏,𝑐𝑐,𝑑𝑏,𝑑𝑑
𝐶13	𝑎,𝑏,𝑐	𝑎,𝑏,𝑐,𝑑	𝑎𝑎,𝑎𝑑,𝑏𝑎,𝑏𝑏,𝑏𝑑,𝑐𝑎,𝑐𝑐,𝑐𝑑	𝑎𝑏,𝑎𝑐,𝑏𝑐,𝑐𝑏,𝑑𝑎,𝑑𝑏,𝑑𝑐,𝑑𝑑
𝐶14	𝑎,𝑏,𝑐	𝑎,𝑏,𝑐,𝑑	𝑎𝑎,𝑎𝑑,𝑏𝑎,𝑏𝑐,𝑏𝑑,𝑐𝑐,𝑐𝑑	𝑎𝑏,𝑎𝑐,𝑐𝑎,𝑐𝑏,𝑑𝑎,𝑑𝑏,𝑑𝑐,𝑑𝑑
𝐶15	𝑎,𝑏,𝑐	𝑎,𝑏,𝑐,𝑑	𝑎𝑎,𝑎𝑑,𝑏𝑎,𝑏𝑐,𝑏𝑑,𝑐𝑎,𝑐𝑏,𝑐𝑑	𝑎𝑏,𝑎𝑐,𝑏𝑏,𝑐𝑐,𝑑𝑎,𝑑𝑏,𝑑𝑐,𝑑𝑑
𝐶16	𝑎,𝑏,𝑑	𝑎,𝑏,𝑐,𝑑	𝑎𝑎,𝑎𝑐,𝑎𝑑,𝑏𝑏,𝑏𝑐,𝑏𝑑,𝑑𝑐	𝑎𝑏,𝑏𝑎,𝑐𝑎,𝑐𝑏,𝑐𝑐,𝑐𝑑,𝑑𝑎,𝑑𝑏,𝑑𝑑
𝐶17	𝑎,𝑏,𝑐,𝑑	𝑎,𝑏,𝑐,𝑑	𝑎𝑎,𝑎𝑐,𝑎𝑑,𝑏𝑎,𝑏𝑐,𝑏𝑑,𝑐𝑑,𝑑𝑐	𝑎𝑏,𝑐𝑎,𝑐𝑏,𝑐𝑐,𝑑𝑎,𝑑𝑏,𝑑𝑑
𝐶18	𝑎,𝑐,𝑑	𝑎,𝑏,𝑐,𝑑	𝑎𝑏,𝑎𝑐,𝑎𝑑,𝑐𝑏,𝑑𝑎,𝑑𝑏,𝑑𝑐	𝑎𝑎,𝑏𝑎,𝑏𝑏,𝑏𝑐,𝑏𝑑,𝑐𝑎,𝑐𝑐,𝑐𝑑,𝑑𝑑
𝐶19	𝑎,𝑐,𝑑	𝑎,𝑏,𝑐,𝑑	𝑎𝑏,𝑎𝑐,𝑎𝑑,𝑐𝑏,𝑐𝑑,𝑑𝑏,𝑑𝑐	𝑏𝑎,𝑏𝑏,𝑏𝑐,𝑏𝑑,𝑐𝑎,𝑐𝑐,𝑑𝑎,𝑑𝑑
𝐶20	𝑎,𝑏,𝑐,𝑑	𝑎,𝑏,𝑐,𝑑	𝑎𝑏,𝑎𝑐,𝑎𝑑,𝑏𝑑,𝑐𝑏,𝑐𝑑,𝑑𝑏	𝑏𝑎,𝑏𝑏,𝑏𝑐,𝑐𝑎,𝑐𝑐,𝑑𝑎,𝑑𝑐,𝑑𝑑
𝐶21	𝑎,𝑏,𝑐,𝑑	𝑏,𝑐,𝑑	𝑎𝑎,𝑏𝑎,𝑏𝑏,𝑐𝑎,𝑐𝑏,𝑐𝑐,𝑑𝑎,𝑑𝑏,𝑑𝑐	𝑎𝑏,𝑎𝑐,𝑎𝑑,𝑏𝑐,𝑏𝑑,𝑐𝑑
𝐶22	𝑎,𝑏,𝑐,𝑑	𝑏,𝑐,𝑑	𝑎𝑎,𝑏𝑎,𝑏𝑏,𝑐𝑎,𝑐𝑏,𝑐𝑑,𝑑𝑎,𝑑𝑏	𝑎𝑏,𝑎𝑐,𝑎𝑑,𝑏𝑐,𝑏𝑑,𝑑𝑐,𝑑𝑑
𝐶23	𝑎,𝑏,𝑐,𝑑	𝑏,𝑐,𝑑	𝑎𝑎,𝑏𝑎,𝑏𝑏,𝑏𝑑,𝑐𝑎,𝑐𝑏,𝑐𝑑,𝑑𝑎	𝑎𝑏,𝑎𝑐,𝑎𝑑,𝑏𝑐,𝑑𝑏,𝑑𝑐,𝑑𝑑
𝐶24	𝑎,𝑏,𝑐,𝑑	𝑏,𝑐,𝑑	𝑎𝑎,𝑏𝑎,𝑏𝑐,𝑏𝑑,𝑐𝑎,𝑑𝑎,𝑑𝑐	𝑎𝑏,𝑎𝑐,𝑎𝑑,𝑐𝑏,𝑐𝑐,𝑐𝑑,𝑑𝑏,𝑑𝑑
𝐶25	𝑎,𝑏,𝑐	𝑎,𝑏,𝑐,𝑑	𝑎𝑎,𝑎𝑑,𝑏𝑎,𝑏𝑏,𝑏𝑑,𝑐𝑎,𝑐𝑏,𝑐𝑑	𝑎𝑏,𝑎𝑐,𝑏𝑐,𝑑𝑎,𝑑𝑏,𝑑𝑐,𝑑𝑑
𝐶26	𝑎,𝑏,𝑐	𝑎,𝑏,𝑐,𝑑	𝑎𝑎,𝑎𝑑,𝑏𝑎,𝑏𝑐,𝑏𝑑,𝑐𝑎,𝑐𝑑	𝑎𝑏,𝑎𝑐,𝑐𝑏,𝑐𝑐,𝑑𝑎,𝑑𝑏,𝑑𝑐,𝑑𝑑
𝐶27	𝑎,𝑏,𝑑	𝑎,𝑏,𝑐,𝑑	𝑎𝑎,𝑎𝑐,𝑎𝑑,𝑏𝑎,𝑏𝑐,𝑏𝑑,𝑑𝑐	𝑎𝑏,𝑐𝑎,𝑐𝑏,𝑐𝑐,𝑐𝑑,𝑑𝑎,𝑑𝑏,𝑑𝑑
𝐶28	𝑎,𝑐,𝑑	𝑎,𝑏,𝑐,𝑑	𝑎𝑏,𝑎𝑐,𝑎𝑑,𝑐𝑏,𝑑𝑏,𝑑𝑐	𝑏𝑎,𝑏𝑏,𝑏𝑐,𝑏𝑑,𝑐𝑎,𝑐𝑐,𝑐𝑑,𝑑𝑎,𝑑𝑑