Coding-Theory

• Error-Correcting Codes: Reed-Solomon, LDPC, and How Distributed Storage Survives Failure · 2025-05-18

  Build error-correcting codes from the ground up: finite field arithmetic, Reed-Solomon encoding and decoding via Lagrange interpolation, LDPC codes and belief propagation, and how modern distributed storage systems use erasure coding to survive disk failures with minimal overhead.

• Shannon's Information Theory from First Principles: Entropy, Channel Capacity, and the Fundamental Limits of Communication · 2025-03-05

  Build Shannon's information theory from the ground up: entropy as a measure of uncertainty, source coding theorem, channel capacity, and the noisy-channel coding theorem that established the theoretical limits of reliable communication.

• Combinatorial Designs and Coding Theory: Block Designs, Steiner Systems, and Finite Geometry · 2022-10-10

  An exploration of combinatorial design theory—block designs, Steiner systems, finite projective planes—and their deep connections to error-correcting codes and experimental design.

• Algebraic Geometry in Computer Science: Gröbner Bases, the Nullstellensatz, and Applications in Cryptography and Coding Theory · 2022-08-21

  A rigorous exploration of how algebraic geometry—Gröbner bases, Hilbert's Nullstellensatz, and elliptic curves—powers modern cryptography, error-correcting codes, and complexity theory.