| Code |
15635
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| Year |
1
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| Semester |
S2
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| ECTS Credits |
6
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| Workload |
TP(45H)
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| Scientific area |
Mathematics
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Entry requirements |
Linear Algebra, Algebra I and Algebra II
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Learning outcomes |
General objectives
1- Learn some fundamental concepts and examples in coding theory.
2- Apply the studied results and techniques in the analysis of several codes;
3- Analyse and understand proofs;
4- Communicate, written and orally, using mathematical language.
Specific objectives:
1-Explain the concepts of alphabet, word, code, transmission channel, and entropy
2- Apply the maximum likelihood decoding method;
3- Calculate the probability of incorrect decoding;
4- Calculate the Hamming distance between two words
5- Apply the minimum distance decoding method
6-Identify the parameters of a code;
7-Identify linear codes;
8-Distinguish the various linear codes studied;
9-Construct the generating matrix and parity matrix from a linear code
10-Apply decoding by Slepian Tables and by Syndrome.
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Syllabus |
CHAPTER 1. Introduction
1.1 First examples and definitions
1.2 Broadcast channels
1.3 Maximum likelihood decoding
1.4 Hamming Distance
1.5 Decoding by nearest neighbour
1.6 Distance of a code
1.7 Main problem in code theory
1.8 Estimates
CHAPTER 2. Linear Codes
2.1 Vector spaces over finite fields
2.2 Parameters and Minimum Weight
2.3 Generating matrix and parity matrix;
2.4 Encoding and decoding
2.5 Equivalence of linear codes
CHAPTER 3. Examples of Linear Codes
3.1 Binary Hamming Codes
3.2 Q-ary Hamming Codes
3.3 Reed-Muller Codes
3.4 Minorant of Gilbert-Varshamov linear
3.5 Golay Codes
3.6 Maximum Separation Distance Codes
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Main Bibliography |
Referências principais
- D. G. Hoffman, K.T. Phelps, D.A. Leonard, C. C. Lindner, C.A. Rodger, J.R. Wall, David Hoffman, Coding Theory: The Essentials (Pure and Applied Mathematics: a Series of Monographs and Textbooks, 150) Marcel Dekker Inc; First Edition (December 1, 1991)
Outras referências
- Cover, T. M., and Thomas, J. A. (2006), Elements of Information Theory (2.ª edição), Wiley
- R. Hill (1997), A First Course in Coding Theory, Oxford University Press
-Ling, S. & Xing, C. (2004). Coding theory: A first course. Cambridge, UK: Cambridge University Press.
- J.H. van Lint (1991), Introduction to Coding Theory, Graduate Texts in Mathematics (3.ª edição), Springer
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Teaching Methodologies and Assessment Criteria |
Teaching/Learning Assessment
- Test 1: 40% (8 points).
- Test 2: 60% (12 points).
The final grade for the course unit results from the sum of the grades obtained in the two defined assessment components. The student passes if they obtain a grade of 9.5 or higher. Otherwise, the student has access to the exam provided they meet a minimum attendance requirement.
Exam Assessment
Exam: 100%.
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Language |
Portuguese. Tutorial support is available in English.
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