Weight distribution of a binary
linear code

You'll find here a way to compute the weight distribution of any binary linear code of dimension ≤ 32 and length ≤ 1024. Note that this is an exhaustive search, hence the time complexity is exponential *O*(2^{k}) on the true dimension *k* of your code. Nevertheless we compute the weight of 64 bits words using 4 access from a 16 bits precalculated table and codewords are generated through a gray code over the Hamming space GF(2,*k*).

Give a generator matrix of your code from a text file which looks exactly like a generator matrix. For a binary code of length *n* and dimension *k*, your file must contain *k *rows of *n* bits, i.e. **0** or **1.** For example, the generator matrix of the simplex code of dimension 4 is represented by:

111111110000000 |

111111110000000 |

111100001111000 |

110011001100110 |

The program will give you the true dimension of your code, i.e. rank(*G*),
where *G* is the generator matrix of your code. The results of the
computation will appear **below** if you do not fill the e-mail address
field, otherwise you'll get them via e-mail.

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Generator matrix file: