Prove that, for a linear code C, either all the code vectors have even weight or exactly
Chapter 6, Problem 6.7.39(choose chapter or problem)
Prove that, for a linear code C, either all the code vectors have even weight or exactly half of them do. [Hint: Let E be the set of vectors in C with even weight and O the set of vectors in C with odd weight. If O is not empty, let co be in O and consider O {co e : e in E}. Show that O O.]
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