"Look at this."
Yuki pointed to a slip of paper on the desk. Strange symbols were written in Mira's handwriting.
"0, 10, 110, 111... what is this?"
Aoi opened their notebook and pondered. "It's a coding pattern. But what does it represent?"
Riku peered at the paper. "A cipher? Mira is mysterious like that."
"Mira left without a word yesterday too," Yuki said. "This code might be a clue."
Aoi began analyzing. "Different lengths. 0 is 1 bit, 10 is 2 bits, 110 and 111 are 3 bits. Variable-length code."
"Variable-length code?"
"Assign short codes to frequently used symbols, long codes to rarely used ones. That's the basis of optimal coding."
Riku clapped his hands. "Like Morse code!"
"Yes. E is just '·' but Q is '--·-'. E is common in English, so it's made shorter."
Yuki thought. "So this code also reflects some frequency?"
"Probably. There's a method called Huffman coding." Aoi drew a diagram on the whiteboard.
"Say we have four symbols A, B, C, D. Their probabilities are 0.5, 0.25, 0.125, and 0.125 respectively."
"A is most common."
"Right. In Huffman coding, you combine symbols starting with the lowest probabilities."
Aoi drew a tree diagram.
"Combine C(0.125) and D(0.125) to get 0.25. Combine that with B(0.25) to get 0.5. Finally combine with A(0.5)."
"And that determines the codes?"
"Assign 0 and 1 to the branches. The path from root to each leaf becomes the code."
Riku copied into his notebook. "So A=0, B=10, C=110, D=111?"
"Perfect. That's Huffman coding."
Yuki looked at Mira's paper again. "So this code is also optimizing something."
"The question is, what symbols?" Aoi pondered.
At that moment, Riku shouted. "Wait! Maybe these aren't letters but concepts."
"Concepts?"
"The four themes Mira always talks about. Entropy, noise, redundancy, coding."
Aoi's eyes lit up. "That's it! What Mira mentions most in this club room is..."
"Entropy," Yuki and Riku answered simultaneously.
"So 0, the shortest code. Next is noise at 10."
Yuki got excited. "The code length represents Mira's degree of interest!"
Aoi calculated. "Average code length is 0.5×1 + 0.25×2 + 0.125×3 + 0.125×3 = 1.75 bits."
"Is that efficient?"
"Calculating entropy... about 1.75 bits. Huffman code is optimal, reaching entropy."
Riku was impressed. "Mira left teaching material as a puzzle."
"No," Aoi's face became serious. "There might be deeper meaning."
Yuki looked at the back of the paper. Small writing.
"Optimal code leads to truth"
"Optimal code leads to truth..."
The three looked at each other.
"What is Mira trying to tell us?" Riku asked.
Aoi said slowly, "In information theory, with optimal coding, the essence of a message becomes visible. Strip away redundancy, and only truth remains."
Yuki nodded. "Maybe Mira wants us to discover something."
"Let's wait for the next hint," Aoi said. "Mira's code must have a continuation."
Yuki carefully tucked the paper into her notebook. Beyond the optimal code, Mira's truth awaits. She believed that.