Prove that, in a binary linear code, either all the codewords have even weight or exactly half even weight and half odd weight.© BrainMass Inc. brainmass.com October 10, 2019, 4:46 am ad1c9bdddf
We wish to prove that in a binary linear code, either all codewords have even weight or half have even weight and half have odd weight.
Let C be a binary linear code. Consider the function defined by
Note that ...
We prove that either all codewords of a binary linear code have even weight or that half have even weight and the other half have odd weight.