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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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