Coding Theory

This document presents an extensive exploration of contemporary coding theory and related applications, aiming to provide an accessible entry point to advanced topics not typically found in standard textbooks. It covers various areas including error correction codes like Fountain, Tornado, LDPC, and Polar codes, discusses coding for distributed storage and locally repairable codes, examines locally decodable and batch codes, introduces expander codes, and explores rank-metric and subspace codes. Additionally, the text touches upon sequences with specific correlation properties, the impact of postquantum cryptography on classical algorithms, and the fundamentals of quantum error-correcting codes. The appendix provides supplementary material on finite geometries, linearized polynomials, and Gaussian coefficients.