Generalized minimum-distance decoding: Difference between revisions

Revision as of 03:19, 10 May 2011

Revision as of 03:20, 10 May 2011

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: <math>\mathbb{E}[X_i^?] = {2\omega_i \over d}</math>and <math>\mathbb{E}[X_i^e] = \Pr[X_i^e = 1] = 1 - {2\omega_i \over d}.</math>

Since <math>c_i \ne C_\text{in}(y_i')</math>, <math>e_i + \omega_i \ge d</math>. This follows [http://www.cse.buffalo.edu/~atri/courses/coding-theory/lectures/lect28.pdf another case analysis] when <math>(\omega_i = \Delta(C_\text{in}(y_i'), y_i)</math> < <math>{d \over 2})</math> or not.

Finally, this implies