If EXTENSION is coded as ONDUXISEX in a certain code, then following the same…

Concept

In alphabet letter-shift coding, each letter of the source word is shifted a fixed number of places along the alphabet based on its position in the word -- here, +10 for a letter in an odd position and -10 for a letter in an even position -- and the shifted letters are written down in the same left-to-right order as the original word. When a shift crosses past Z or before A, it wraps around the 26-letter cycle.

Applying the rule to EXTENSION -> ONDUXISEX

1. E (position 1, odd) + 10 = O

2. X (position 2, even) - 10 = N

3. T (position 3, odd) + 10 = D (20 + 10 = 30; 30 - 26 = 4, the 4th letter, wrapping past Z)

4. E (position 4, even) - 10 = U

5. N (position 5, odd) + 10 = X

6. S (position 6, even) - 10 = I

7. I (position 7, odd) + 10 = S

8. O (position 8, even) - 10 = E

9. N (position 9, odd) + 10 = X

Reading these off in order gives O N D U X I S E X, which is exactly ONDUXISEX -- confirming the rule: odd-position letters shift +10, even-position letters shift -10.

Applying the same rule to MATRIMONIAL

1. M (position 1, odd) + 10 = W

2. A (position 2, even) - 10 = Q

3. T (position 3, odd) + 10 = D

4. R (position 4, even) - 10 = H

5. I (position 5, odd) + 10 = S

6. M (position 6, even) - 10 = C

7. O (position 7, odd) + 10 = Y

8. N (position 8, even) - 10 = D

9. I (position 9, odd) + 10 = S

10. A (position 10, even) - 10 = Q

11. L (position 11, odd) + 10 = V

Cross-check

Re-verifying the wrap-around step independently: T is the 20th letter of the alphabet, and 20 + 10 = 30; since the alphabet has only 26 letters, subtracting 26 gives 4, the 4th letter, D -- the same wrap-around used for EXTENSION's T -> D. Likewise, A is the 1st letter, and 1 - 10 = -9; adding 26 gives 17, the 17th letter, Q -- consistent throughout both words.

Reading off each transformed letter of MATRIMONIAL in order gives W Q D H S C Y D S Q V, which matches WQDHSCYDSQV.