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Learning outcomes |
General objectives
- Learn some fundamental concepts and examples in code theory and cryptography;
- Apply the results and techniques studied in the analysis of various codes;
- Analyze and understand demonstrations;
- Communicate, written and orally, using mathematical language.
Specific objectives:
Learn some concepts of Elementary Number Theory
- Learn some fundamental concepts and examples in code theory and cryptography
-Explain the concepts of the alphabet, word, code, transmission channel, and entropy
- Apply the maximum likelihood decoding method;
- Calculate the probability of incorrect decoding;
- Calculate the Hamming distance between two words
- Apply the minimum distance decoding method
-Identify the parameters of a code;
-Identify and use linear codes;
-Build the generator matrix and parity matrix of a linear code
-Apply the decoding by Slepian Tables and by Syndrome.
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Main Bibliography |
- 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
- J. P. Hoffstein, J. Pipher e J. H. Silverman (2014), An Introduction to Mathematical Cryptography (2.ª edição), Springer
- Koshy T., "Elementary Kumber theory with Applications", 2nd Edition, Harcourt, Academic Press, 2007
-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
-Rosen, K., Elementary Number Theory and Its Applications, 6th Edition. Addison-Wesley Publishing Company. 2018.
-Santos, J.O., Introdução à Teoria dos Números, IMPA, Colecção Matemática Universitária. 2000.
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Teaching Methodologies and Assessment Criteria |
The typology of the classes is theoretical-practical: the exposition of the material by the teacher, interspersed with the resolution of tasks by the students under the guidance of the teacher. It is intended that students, in an autonomous way, analyze, discuss and apply the main concepts covered.
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