Errata - Applied Discrete Structures - V3.5

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.

Version 3.5 - May 2018

• Section 2.3. In the comment below Theorem 2.3.4, $$= \emptyset$$ is missing in ... where $$A_i \cap A_j = \emptyset \dots$$ (thanks to Steve Sadler, Bellevue College)
• Section 6.4, Example 6.4.7. The entry in row P3, column C1 of the matrix or $$rs$$ should be 0, not 1.
• Section 12.6 The right side of the third equation at the end of the third paragraph should be 1, not 0. The rest of this intital example is consistent with this change.
• Section 15.5, Exercise #3. The original version was missing part (e), although there was a solution given for that part. I've added both (e) and a bonus part (f). Also have clarified the solution.

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. $$(1,0,0,0,1,1)$$

2. $$(1,0,1,0,1,1)$$

3. $$(0,1,1,1,1,0)$$

4. $$(0,0,0,1,1,0)$$

5. $$(1,0,0,0,0,1)$$

6. $$(1,0,0,1,0,0)$$

Solution:

1. Syndrome = $$(1,0,1)$$. Corrected coded message is $$(1,1,0,0,1,1)$$ and original message was $$(1, 1, 0)$$.

2. Syndrome = $$(1,1,0)$$. Corrected coded message is $$(0,0,1,0,1,1)$$ and original message was $$(0, 0, 1)$$.

3. Syndrome = $$(0,0,0)$$. No error, coded message is $$(0,1,1,1,1,0)$$ and original message was $$(0, 1, 1)$$.

4. Syndrome = $$(1, 1,0)$$. Corrected coded message is $$(1,0,0,1,1,0)$$ and original message was $$(1, 0, 0)$$.

5. Syndrome = $$(1,1,1)$$. This syndrome occurs only if two bits have been switched. No reliable correction is possible.

6. Syndrome = $$(0,1,0)$$. Corrected coded message is $$(1,0,0,1,1,0)$$ and original message was $$(1, 0, 0)$$.

Errata for V2.0----Errata for V3.0----Errata for V3.3----Errata for V3.3----No V3.4