Lecture Notes
| Lecture | Lecture Notes | Topics | |
|---|---|---|---|
| 1 | Error Detection Schemes (.pdf file) | PostNET, ISBNs, UPC, BookLand, Bank Check, Check Sum Schemes | |
| 2 | Introductory Concepts (.pdf file) | History, Bell Labs, Hamming quote, Repeat Code, Block codes error detecting, error correcting, single error correcting example |
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| 3 | Combinatorics in Space (.pdf file) | Mariner 9 Telemetry Specifications | |
| 4 | Basic Theory (.pdf file) | Hamming distance, settings, minimum distance, weight covering radius, packing radius, sphere packing bound, equivalent codes |
|
| 5 | Math Meets the Bookies (.pdf file) | Codes with covering radius 1 | |
| 6 | Linear Codes (.pdf file) | Linear codes, equivalence of linear codes, generator matrix parity check matrix, Singleton bound, Hamming codes |
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| 7 | Decoding Linear Codes (.pdf file) | Syndromes,Hamming decoding, code cosets, syndrome decoding | |
| 8 | Finite Fields (.pdf file) | Definitions, basic properties, constructions, subfields, automorphisms | |
| 9 | A 2-error correcting code (.pdf file) | Example of a length 15 binary BCH code | |
| 10 | Cyclic Codes I (.pdf file) | Definition, Examples, Rings, Polynomial Rings, Ideals, Principal Rings Ideals and Cyclic Codes, Generator polynomials |
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| 11 | Cyclic Codes II (.pdf file) | Generator matrix, Dual Code, Parity Check Matrix, Syndromes, Error Trapping | |
| 12 | Polynomials (.pdf file) | Minimal polynomials, Cyclotomic Cosets, factoring xn - 1 | |
| 13 | Idempotents & Binary Cyclic Codes (.pdf file) | Idempotent generators, Minimal Ideals, Examples | |
| 14 | MDS Codes (.pdf file) | Maximum Distance Separable Codes, Projective Geometry, Ovals, Normal Rational Curves | |
| 15 | Reed-Muller Codes (.pdf file) | Recursive Definition, (u,u+v)-construction, Properties, Examples, Reed Decoding Geometric View, Flats in AG(n,2), Mariner 9 Application | |
| 16 | Designs and Codes (.pdf file) | BIBD's, Examples, Parameters, t-Designs, Derived Designs, Complementary Designs Designs in Codes, Perfect Codes, Self-Orthogonal Codes, Doubly Even Codes Self-Dual Codes, Golay Codes, Assmus-Mattson Theorem, Extremal Codes |