if , decode code word to be all 1's

This algorithm is a boolean function in its own right, the majority function.

Example

In a code, if R=[1 0 1 1 0], then it would be decoded as,
* , , so R'=[1 1 1 1 1]
* Hence the transmitted message bit was 1.

References

#Rice University, https://web.archive.org/web/20051205194451/http://cnx.rice.edu/content/m0071/latest/