As significant mathematics errors appear, they will be logged here. Most of the typographical errors (missing/extraneous spaces, mathematics in non-math font, etc.) are not listed.
\( = \emptyset\)is missing in
... where \(A_i \cap A_j = \emptyset \dots\)(thanks to Steve Sadler, Bellevue College)
3. If the error-correcting code from this section is being used, how would you decode the following blocks? Expect an error that cannot be fixed with one of these.
\((1,0,0,0,1,1)\)
\((1,0,1,0,1,1)\)
\((0,1,1,1,1,0)\)
\((0,0,0,1,1,0)\)
\((1,0,0,0,0,1)\)
\((1,0,0,1,0,0)\)
Solution:
Syndrome = \((1,0,1)\). Corrected coded message is \((1,1,0,0,1,1)\) and original message was \((1, 1, 0)\).
Syndrome = \((1,1,0)\). Corrected coded message is \((0,0,1,0,1,1)\) and original message was \((0, 0, 1)\).
Syndrome = \((0,0,0)\). No error, coded message is \((0,1,1,1,1,0)\) and original message was \((0, 1, 1)\).
Syndrome = \((1, 1,0)\). Corrected coded message is \((1,0,0,1,1,0)\) and original message was \((1, 0, 0)\).
Syndrome = \((1,1,1)\). This syndrome occurs only if two bits have been switched. No reliable correction is possible.
Syndrome = \((0,1,0)\). Corrected coded message is \((1,0,0,1,1,0)\) and original message was \((1, 0, 0)\).