In this communication, we present the construction of a [7 4 2] - linear code which is an extended code of the [ 6 4 1 ] code and is in one-to-one correspondence with the known [ 7 4 3 ] - Hamming code. Our construction is due to the Cayley table for of the generated points of as permutations of the -avoiding patterns of the non-associative AUNU schemes as reported by the authors earlier. First, the Cayley table for is converted to a matrix say in the binary system using arithmetic. The matrix which is of order is then shown to generate a linear code of size. Next, echelon row operations are used to transform into a standard generator matrix say , for a [ 6 4 1 ] code. Finally, the [6 4 1] code is extended to obtain the desired [7 4 2]-linear Code which is in one-to-one correspondence with the known [ 7 4 3 ]- Hamming code.