Table 1 Polynomial-based DNA sequences generated by BCH codes over Galois ring and field extensions.

From: Ancient DNA sequence revealed by error-correcting codes

Tables DNA sequences GI number Organism L R-F Primitive polynomial Generator polynomial
S02.a) TS 45269853 Sc D/F x3+ax2+bx+b x6+x5+1
S02.b) TS 45269853 Sc B/R x6+x4+x3+x+1 x6+2x5+x4+x3+3x+1
S02.c) TS* 78096542 Ts D/F x3+bx2+x+a x6+x5+x4+x+1
S02.d) TS* 78096542 Ts C/R x6+x5+x4+x+1 x6+x5+x4+2x2+3x+1
S02.e) TS* 632733 Nt A/R x6+x5+x2+x+1 x6+3x5+2x4+x2+x+1
S02.f) TS* 632733 Nt A/R x6+x5+x3+x2+1 x6+3x5+x3+x2+2x+1
S02.g) TS 7328566 Cs B/R x6+x5+1 x6+3x5+2x3+1
S02.h) TS* 186509758 At A/R x6+x5+x3+x2+1 x6+3x5+x3+x2+2x+1
S02.i) PM 832917 Sc A/R x6+x5+x2+x+1 x6+3x5+2x4+x2+x+1
S02.j) TS 12587 Hs C/R x6+x5+1 x6+3x5+2x3+1
2a and b ? 30695458 At C/R x10+x9+x8+x7+x6+x4+x3+x+1 x10+x9+x8+3x7+x6+x4+x3+3x+1
3.a) TS 217937 Ib B/R x3+ax2+ax+a x6+x5+x3+x2+1
3.b) TS 51093376 Pd D/F x3+ax2+bx+b x6+x5+1
3.c) TS 16740522 Mm A/R x6+x5+x4+x+1 x6+x5+x4+2x2+3x+1
3.d) ? 25140446 Hs B/R x6+x5+1 x6+3x5+2x3+1
  1. Abbreviations: TS targeting sequence; PM protein motifs; L labelings A, B, C and D; R ring; F field; *signal or transit peptide without experimental evidence. Sc Saccharomyces cerevisiae; Ts Triticum aestivum; Nt Nicotiana tabacum; Cs Citrus sinensis; At Arabidopsis thaliana; Hs Homo sapiens; Ib Ipomoea batatas; Pd Polistes dominulus; Mm Mesobuthus martensii.