The (33,16) Doubly-Even Self-Orthogonal Codes
In this site, we give the 594 inequivalent (33,16) doubly-even
self-orthogonal codes over GF(2) that do not contain a coordinate of zeros.
We use a table of weight distributions to
navigate through the site.
The weight distribution table contains one entry for each of the different
possibilities for the weight distribution of a (33,16) doubly-even
self-orthogonal code.
Included in each entry is:
- Weight Distribution : Since our codes are doubly-even, we only list
the 0 modulo 4 weights. The weight distribution of the orthogonal complement of
each code C can easily be worked from the weight distribution of C since the
number of weight 33-4i words in the orthogonal complement is equal to the
number of weight 4i words in C.
- Number of Codes : the number of codes with the given weight
distribution.
- List Number : a unique list number. Click the list number to get a
code list table containing one entry for each of the codes with the given weight
distribution.
Included in each entry in the code list table is:
- Code Number: a unique code number. Click the code number to load
the codes document.
- Code Type: a number used to identity the type of the
code. We use the weight 4 words contained in each code to classify the distance
4 codes as either d_i-codes or e_i-codes (for more on this, see my phd thesis).
If the code is a d_i-code then Code Type has the value i, if the code is an
e_i-code then Code Type has a value of -i, and if the code is a distance 8 code
then Code Type has a value of 0.
- Group Size: the size of the codes automorphism group.
The document for each code contains the following information:
- A (partial) generator matrix: a 16 by 17 matrix A. The matrix
[I|A], where I is a 16 by 16 identity matrix, generates the code.
- Generators for the automorphism group: : a list of permutations
that generates the automorphism group of the code.
Each generator is written as a product of disjoint cycles.
Each generator is a permutation of the integers 0,1,...,32.
The integers 0,1,...,15 represent the coordinates in the code that correspond to
the identity matrix I.
The integers 16,17,...,32 represent the coordinates in the code that correspond
to the matrix A.
Each code also contains the code number, the code type, the codes weight
distribution, the size of the codes automorphism group, and links to the
previous code and the next code in our list.
Click here to download all the codes and
groups at one time.