We give a new construction of the extended binary Golay code. The code is constructed as a zero divisor code over the dihedral group of twenty-four elements, D24. The construction is algebraic, much like the construction of the (23,12,7) binary Golay code from a polynomial.

A new construction method for codes using encodings from group rings is presented. They consist primarily of two types, zero-divisor and unit-derived codes. Previous codes from group rings focused on ideals; e.g. cyclic codes are ideals in the group ring over a cyclic group. The fresh focus is on the encodings themselves, which only under very limited conditions result in ideals. Using an isomorphism between group rings and a certain well- defined ring of matrices, equivalent matrix codes are established with resulting generator and check matrices. Group rings are a fruitful source of units and zero-divisors from which new codes result. Many code properties may more easily be expressed in terms of group ring properties.