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In this case, <math>\mathbb{E}[X_i^?] = \tfrac{2\omega_i}{d}</math> and <math>\mathbb{E}[X_i^e] = \Pr[X_i^e = 1] = 1 - \tfrac{2\omega_i}{d}.</math>
Since <math>c_i \ne C_\text{in}(y_i'), e_i + \omega_i \geqslant d</math>. This follows [http://www.cse.buffalo.edu/~atri/courses/coding-theory/lectures/lect28.pdf another case analysis] {{Webarchive|url=https://web.archive.org/web/20110606191851/http://www.cse.buffalo.edu/~atri/courses/coding-theory/lectures/lect28.pdf |date=2011-06-06 }} when <math>(\omega_i = \Delta(C_\text{in}(y_i'), y_i) < \tfrac{d}{2})</math> or not.
Finally, this implies
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==References==
* [http://www.cse.buffalo.edu/~atri/courses/coding-theory/lectures University at Buffalo Lecture Notes on Coding Theory – Atri Rudra]{{Dead link|date=August 2025 |bot=InternetArchiveBot |fix-attempted=yes }}
* [http://people.csail.mit.edu/madhu/FT01 MIT Lecture Notes on Essential Coding Theory – Madhu Sudan]
* [http://www.cs.washington.edu/education/courses/cse533/06au University of Washington – Venkatesan Guruswami]
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