15.2 Message Intersections & Conditional Coding Tables

Message Intersections & Conditional Coding Tables

3. Fictitious Language / Message Elimination Coding

In these exercises, assume a fixed one-to-one word substitution with scrambled order. Three or four sentences are paired with code words. The solution requires systematic pairwise intersection to isolate words appearing in multiple statements.

Statement 1: "signal track clear route"  -->  "pe ka zo ti"
Statement 2: "route green proceed loco"  -->  "zo da ma lu"
Statement 3: "clear signal loco fast"    -->  "ti pe lu ba"
Statement 4: "fast train proceed green"  -->  "ba da ma wo"

• Elimination Protocol:
  1. Compare Statement 1 and Statement 2: The only common word is "route"; the only common code is "zo". Thus, $\text{route} = \text{zo}$.
  2. Compare Statement 1 and Statement 3: Common words are "signal" and "clear"; common codes are "ti" and "pe". Thus, $\{\text{signal}, \text{clear}\} = \{\text{ti}, \text{pe}\}$.
  3. In Statement 1, three words and codes are identified ("route" = "zo", "signal" / "clear" = "ti" / "pe"). The sole remaining word is "track", and the sole remaining code is "ka". Thus, $\text{track} = \text{ka}$.
  4. Compare Statement 2 and Statement 3: Common word is "loco"; common code is "lu". Thus, $\text{loco} = \text{lu}$.
  5. Compare Statement 3 and Statement 4: Common word is "fast"; common code is "ba". Thus, $\text{fast} = \text{ba}$.

4. Conditional Matrix Coding

A master table maps characters/digits to specific symbols or letters. Candidates must apply a set of conditional clauses with strict logical priority before writing the output:

• Condition 1: If the first element is a vowel and the last element is a consonant, their codes are interchanged.
• Condition 2: If both the first and last elements are even numbers, both are to be coded as $\delta$.
• Condition 3: If an odd number is immediately preceded as well as immediately followed by a symbol, that odd number is coded as $\#$.

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Worked Example 3: Conditional Matrix Coding

Problem: Digits are coded as symbols: $1:@, 2:\text{\textdollar}, 3:\%, 4:\&, 5:\#, 6:*, 7:\uparrow, 8:\Delta, 9:\copyright$.

• Condition 1: If the first digit is odd and the last digit is even, their codes are interchanged.

• Condition 2: If both the first and last digits are odd, both are coded as $\Omega$. Find the code for the number $746823$.

• Step 1: Examine Boundary Digits: First digit $= 7$ (odd). Last digit $= 3$ (odd).

• Step 2: Check Applicability of Conditions:

  • Condition 1 requires first odd and last even. Not met.
  • Condition 2 requires both first and last digits to be odd. Met!

• Step 3: Apply Condition 2: Both the first ($7$) and last ($3$) digits are replaced by $\Omega$.

• Step 4: Code Intermediate Digits via Master Table:

  • $4 \to \&$
  • $6 \to *$
  • $8 \to \Delta$
  • $2 \to \text{\textdollar}$

• Step 5: Synthesize Output Code:

$$\Omega \quad \& \quad * \quad \Delta \quad \text{\textdollar} \quad \Omega$$

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Preserve ambiguity when the evidence does not distinguish words

Message coding commonly uses a fixed one-to-one substitution with scrambled word order. That assumption must be stated or clear from the exercise. Shared words imply shared code sets, but two shared words and two shared codes do not establish the individual pairings. Record an unresolved pair instead of guessing.

For example, suppose 'red train moves' is coded as 'ka zo pe' and 'blue train stops' as 'ti zo lu'. Their only common word is train and only common code is zo, so train maps to zo. The first sentence leaves red and moves paired with ka and pe in an unknown order. A third sentence, 'red light shines', coded as 'ka mi nu', isolates red as ka. Moves must then be pe.

Each deduction uses intersection followed by elimination. No positional match was used: the code appearing first is not necessarily the first word. If a question asks only for train, the first two sentences suffice. If it asks for red, the third sentence provides the missing distinction. Adequacy depends on the target, not on whether every code has been decoded.

For conditional tables, begin by copying the base mapping. Then list every condition, check the boundary characters and apply the stated priority. A condition can replace, swap or duplicate codes. These are different operations. Swapping endpoint codes keeps both original codes but exchanges their positions; replacing both endpoints by one symbol discards their individual base codes.

If two conditions can apply and the question supplies no priority or rule for combining them, do not invent one. Test whether they happen to produce the same output; otherwise the exercise needs clarification. Where the conditions are mutually exclusive, no priority conflict arises.

A useful final check compares input and output length, verifies unaffected middle positions against the table, and confirms that only the intended endpoints changed. This catches a correct condition applied to the wrong positions.