We proposed previously a cyclic code made of 22 triplets, which we now call the AB code. It is made up of the following chain: AUGGUGCCAUUCAAGACUAUGA. The letters A, U, C, G represent the classical symbols of the (purine and pyrimidine) bases of the genetic code. This chain presents the following features: (1) when it is in cyclic form, it begins with the initiation codon AUG, ends with the termination codon UGA, and it can be read triplet after triplet by choosing 1 and only 1 representative of each synonymy class in the classical degenerate genetic code made of 64 triplets. The chain, therefore, possesses 1 and only 1 codon for each amino-acid; (2) except for the doublet CG, triplets of the chain begin with the 15 other possible doublets of bases (satisfying the "wobble" hypothesis presented by Crick); (3) it corresponds (except for 1 base) to the "loop" part of the CEnothera mitochondrial Gly-tRNA; (4) it can be modified, without loss of the properties (1) and (2), in such a way as to have 15 bases in common with the loop part of other mitochondrial tRNA's considered as primitive, like Ala-, Pro- and Arg-tRNA; (5) it contains the most frequent triplets, but not the most rare ones, appearing in the genome of numerous species; (6) it exhibits a coherent internal structure with respect to the molecular weight of its triplets. This structure, also found in the loop part of mitochondrial tRNA's, contains an excess of AU bases with respect to GC bases. This fact has no explanation in the classical probabilistic model of the tRNA's. Therefore, we propose the cyclic AB code as a primitive genetic structure with the essential coding properties of the present genetic code.