Classifying subspaces of Hamming spaces

The codes classified in the paper can here be obtained electronically. The following codes with minimum distance greater than or equal to 3 are classified: binary codes up to length 14, ternary codes up to length 11, and quaternary codes up to length 10.

The parity check matrices of the codes are given, with the identity matrix part omitted. The first three lines of the files contain, respectively, the number of codes, the value of k (the dimension), and the value of r (the codimension). Then the parity check matrices are listed one by one using k rows of length r. To get an r x n parity check matrix, transpose these rows and add the r columns of the identity matrix.

For the binary and ternary codes, the field elements are the integers modulo q. For the quaternary codes, the field elements are {0,1=1,2=a,3=a+1}, where a is a primitive element.

An [n,k,d] code is a code with length n, dimension k, and minimum distance at least d. Please note that in the definition of equivalence for quaternary codes, we allow global conjugacy in addition to monomial transformations. (So there are here fewer inequivalent quaternary codes than in other published studies that use only monomial transformations.)

Binary codes

Ternary codes

Quaternary codes

Last update: August 7, 2002 by Patric Östergård.