Decipherability of codes Original Research Article

Several forms of decipherability of codes, like unique decipherability, multiset decipherability and set decipherability are subsumed under a general concept of decipherability using varieties of monoids. A Galois connection is established between classes of codes and varieties of monoids, establishing a measure of the decipherability of a class of codes. Several well-known classes of codes are shown to be varieties, and several varieties of monoids are shown to be codifiable. Examples are also given of non-codifiable varieties of monoids. The simplified domino graph of a code is constructed, and it is shown that the language it accepts forms a basis for the variety of monoids associated with the code.