As ALS progresses, patients lose motor skills and become reliant on eye movements for communication. Effective tools for severe ALS must be minimal-effort, error-tolerant, and accessible. We present an eye-tracking system that maps left/right gaze movements to binary codewords encoding 24 essential daily keywords via Huffman or max-heap trees. Keywords are partitioned into two groups of 12, yielding short codewords (3--4 bits for Huffman, 1--3 bits for max-heap) that reduce gaze actions by 52--70 % compared to conventional QWERTY-based dwell selection. Unlike existing systems requiring expensive IR-based trackers, our approach classifies gaze into only two directions, enabling standard webcam use. Error-tolerant communication is supported through adaptive thresholds, FIR filtering, and Huffman-based error detection (91.7 % and 95.8 % for single-bit deletion and insertion errors). When an error is detected, a top-k candidate correction mechanism achieves up to 97.2 % correction accuracy with one additional gaze action. Testing with 11 participants aged 10 to 80 achieved a character error rate of 1.3 % and an average detection time of 1.77 seconds per character.