Duration: 35 1-hour lectures (12 weeks, 3hrs/week)

(1 lecture for midterm makes total 36)

(comments: undergraduate level, covers most coding theory topics at an appropriate level, does not cover algebra in enough detail)

(comments: graduate level, covers many topics not covered in the course, has better detail on some topics needed for course)

(comments: does not cover some topics for coding theory, good algebra reference, not directly referenced for lectures, but would make a good resource)

**Resources:**

**Lecture 1: Overview and Introduction to Coding Theory**

Text: 1.1

Reserve Text: Introduction (pages 1 - 8)

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**Lecture 2: Basic Concepts**

Text: 1.2 - 1.5

Reserve Text: 2.1, 3.3

**Lecture 3: Decoding Strategies**

Text: 1.6 - 1.10

Reserve Text: 4.1, 4.2

**Lecture 4: Error Correcting Capabilities **

Text: 1.11 - 1.12, 3.1

Reserve Text: 4.1, 4.2, and pages 136, 139, 175

**Lecture 5: Algebraic Background**

Text: Section 5.1

Reserve Text: Appendix A1, 7.1

**Lecture 6: Introduction to Finite Fields **

Text: Section 5.1

Reserve Text: 7.1, Appendix A1

**Lecture 7: Introduction to Finite Fields II**

Text: Section 5.1

Reserve Text: 7.1, Appendix A1

**Lecture 8: Polynomials over Finite Fields**

Text: Section 5.1

Reserve Text: 7.2, Appendix A1, A4

**Lecture 9: Construction of Finite Fields **

Text: Section 5.1

Reserve Text: 7.1, Appendix A1

**Lecture 10: Properties of Finite Fields**

Text: Section 5.1

Reserve Text: 7.1, 7.3, Appendix A1

**Lecture 11: Finite Field Related Examples**

Text: Section 5.1

Reserve Text: 7.1, 7.3, Appendix A1

**Lecture 12: Linear Codes **

Text: Chapter 2

Reserve Text: 5.1, 5.2

**Lecture 13: Properties of Linear Codes**

Text: Section 2.6, 2.8

Reserve Text: 5.1, and pages 143-144

**Lecture 14: The Dual Code**

Text: section 2.7

Reserve Text: 5.1

**Lecture 15: Perfect Codes**

Text: Sections 3.1 - 3.3

Reserve Text: 5.1, 6.1 and pages 138, 150, 154

**Lecture 16: Hamming Codes**

Text: Sections 3.1 - 3.3

Reserve Text: 6.1

**Lecture 17: Decoding Linear Codes, Analysing Algorithms**

Text: 2.10 - 2.12

Reserve Text: 5.1, 5.3

**Lecture 18: Decoding Linear Codes with Analysis**

Text: Sections 2.10 - 2.12

Reserve Text: 5.1, 5.3, Appendix A1

**Lecture 19: Extended Binary Golay Code **

Text: Sections 3.5 - 3.7

Reserve Text: page 151

**Lecture 20: Algebraic Background for Cyclic Codes**

Text: --

Reserve Text: Appendix A1

**Lecture 21: Algebraic Background for Cyclic Codes II **

Text: --

Reserve Text: Appendix A1

**Lecture 22: Cyclic Codes**

Text: Sections 4.1 - 4.2

Reserve Text: 7.3, 7.4

**Lecture 23: Dual Code for Cyclic Codes **

Text: Section 4.5

Reserve Text: 7.4

**Lecture 24: Burst Error Correcting**

Text: Section 7.1

Reserve Text: 7.5

**Lecture 25: Interleaving**

Text: Section 7.2

Reserve Text: 7.5

**Lecture 26: Erasures**

Text: Section 6.6

Reserve Text: --

**Lecture 27: Minimal Polynomials**

Text: Section 5.2

Reserve Text: 7.2, Appendix A1, A4

**Lecture 28: Minimal Polynomials CONT'D**

Text: 5.2

Reserve Text: 7.2, Appendix A1, A4

**Lecture 29: Cyclotomic Cosets**

Text: --

Reserve Text: 7.3

**Lecture 30: BCH Codes**

Text: 5.4

Reserve Text: 8.1

**Lecture 31: BCH Decoding Algorithm**

Text: 5.5

Reserve Text: 8.1

**Lecture 32: Reed-Solomon Codes**

Text: Chapter 6

Reserve Text: 8.2

**Lecture 33: Application of Reed-Solomon Codes**

Text: Section 7.3, Appendix C

Reserve Text: --

**Lecture 34: Final Exam Review**

**Lecture 35: Overflow/Holiday Allowance **