Generalized minimum-distance decoding: Difference between revisions

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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 [httpanother case analysis<ref>{{cite web|url=https://www.cse.buffalo.edu/~faculty/atri/courses/coding-theory/lectures/lect28.pdf another|title=Lecture case28: analysis]Generalized Minimum Distance Decoding {{Webarchive|date=November 5, 2007 |archive-url=https://web.archive.org/web/20110606191851/http://www.cse.buffalo.edu/~atri/courses/coding-theory/lectures/lect28.pdf |archive-date=2011-06-06 |url-status=live}}</ref> 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==

{{Reflist}}

* [httphttps://www.cse.buffalo.edu/~faculty/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]