Coding and Expansion Foundations¶
This course builds the five foundations needed to read the Conjecture 3 research map fluently:
- classical linear codes over GF(2)
- Tanner graphs and LDPC structure
- expander graphs and graph cuts
- CSS and QLDPC constructions
- syndrome extraction under hardware constraints
It is intentionally not a general coding-theory textbook. It is a personalized bridge from stabilizer/surface-code intuition into the QLDPC barrier research program.
Course Outcome¶
After this course, the learner should be able to explain why expander-style QLDPC codes create a routing bottleneck on static near-square 2D hardware, identify which pieces of the Conjecture 3 program are already theorem-backed, and locate the remaining open gaps around compiler-native CD(T_n, G) semantics.
The follow-on course is Conjecture 3 Frontier Alignment. Start it only after completing this course or passing the completion diagnostic.
Fresh-Start Lessons¶
Use these files as the learner-facing course. They regenerate the Heptabase material from scratch, correct loose or broken parts, and add the missing final course material.
- Lesson 01 - Research Orientation, GF(2), and the Hamming Code - next
- Lesson 02 - Matrices, Duals, Parameters, and Local Operations - ready
- Lesson 03 - CSS Codes, Tanner Graphs, LDPC, and Locality - ready
- Lesson 04 - Girth, Local Views, Tanner Codes, and Small-Set Expansion - ready
- Lesson 05 - CSS Tanner Graphs, Spectra, and the Petersen Graph - ready
- Lesson 06 - Expansion, Cuts, Ramanujan Graphs, and 2D Grids - ready
- Lesson 07 - CSS and QLDPC Codes - ready
- Lesson 08 - Syndrome Extraction and Hardware Constraints - ready
- Lesson 09 - Reading the Conjecture 3 Research Map - ready
The old sessions/ files remain as compact historical plans. They are not the fresh-start learner path.
Progress¶
Assessment¶
Use the rubric after the lesson path, or as a placement test if the learner wants to skip directly into the frontier course.
Textbook Chapters¶
- 01 - Classical Linear Codes Over GF(2)
- 02 - Tanner Graphs and Code Structure
- 03 - Expander Graphs and Graph Cuts
- 04 - CSS and QLDPC Codes
- 05 - Syndrome Extraction and Hardware Constraints
- 06 - Integration: Reading the Research Map
Source Trace¶
The historical Heptabase source map is here. Use it as provenance and teaching-style evidence, not as the authoritative mathematical source. The lesson mismatch is explained there: Heptabase had seven AI Tutor sections, but each section contained multiple finer lesson parts.