COM-102: Advanced information, computation, communication II

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Lectures in this course (54)

Explores finite fields, vector spaces, commutative groups, and field properties, highlighting their significance in coding theory and algebraic computations.

Finite Fields and Vector Spaces

Explores finite fields, isomorphisms, and vector spaces over finite fields.

Vector Spaces: Definitions and Examples

Covers vector spaces, subspaces, linear independence, and spans in finite-dimensional spaces.

Linear Independence and Basis

Explains linear independence, basis, and matrix rank with examples and exercises.

Linear Codes: Dimension and Hamming Weight

Discusses linear codes' dimension and Hamming weight with examples and theorems.

Binary Parity Check Code

Explores binary parity check codes, systematic generator matrix, and Gaussian elimination.

Linear Block Codes: Basics

Covers the basics of linear block codes and systematic codes over a field F.

Error Correction Codes: Syndrome and Hamming Codes

Explains error correction codes, syndromes, Hamming codes, and error correction techniques.

Coset Decoding: Theory and Examples

Covers the theory of coset decoding and how to decode received messages.

Cosets & Syndromes: Error Probability in Linear Codes

Explores cosets, syndromes, and error probability in linear codes.

Reed Solomon Codes: Basics and Applications

Introduces Reed Solomon Codes, their applications, polynomial definitions, interpolation, roots, and the Fundamental Theorem of Algebra.

Error-Correcting Codes: Reed-Solomon

Explains Reed-Solomon error-correcting codes and their unique decoding property over finite fields.

Reed-Solomon Codes: Construction and Properties

Explores Reed-Solomon codes' construction, properties, decoding examples, linear codes, and applications in error correction on optical disks.

Information Theory: Source Coding, Cryptography, Channel Coding

Covers source coding, cryptography, and channel coding in communication systems, exploring entropy, codes, error channels, and future related courses.

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