Type A
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Code |
Competences Specific | | FB1 |
Be able to solve mathematical problems that may arise in engineering. Have the ability to apply knowledge on: linear algebra, differential and integral calculation, numerical methods, numerical algorithmics, statistics and optimisation.
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| FB3 |
Understand and master the basic concepts discrete mathematics, logic, algorithmics and computational complexity, and their application in solving problems inherent in engineering.
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Type B
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Code |
Competences Transversal | | B2 |
Have knowledge in basic and technological subjects, which gives them the ability to learn new methods and theories, and the versatility to adapt to new situations. |
Type C
|
Code |
Competences Nuclear |
Type A
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Code |
Learning outcomes |
| FB1 |
Know how to work with polynomials and analyse divisibility relationships.
Be familiar with the concept of linear code and know how to handle the generating and control matrices of a linear code.
Understand the Hamming codes and know how to construct them.
Be familiar with and know how to apply linear code error correction by syndrome.
Know the cyclical codes and understand the concept of generator polynomial of a cyclical code. Know how to perform the basic operations of a code using the cyclical polynomial.
Be familiar with and know how to construct and work with algebraic code, Reed Solomon code and BCH code.
| | FB3 |
Know the concepts of divisibility, prime numbers and greatest common divisor. Know how to factorise an integer and determine its primality and know how to calculate the greatest common divisor.
Know the Bézout's identity of two integers and know how to calculate the coefficient using Euclid's algorithm.
Be familiar with and know how to handle the congruencies of integers and Zm rings.
Know how to work with polynomials and analyse divisibility relationships.
Be familiar with and know how to handle finite bodies.
Distinguish and determine primitive elements of a finite body.
Know the concepts of block code, Hamming distance, length and correcting capacity.
Know the most significant milestones that relate corrective capacity and code length.
Be familiar with the concept of linear code and know how to handle the generating and control matrices of a linear code.
Understand the Hamming codes and know how to construct them.
Be familiar with and know how to apply linear code error correction by syndrome.
Know the cyclical codes and understand the concept of generator polynomial of a cyclical code. Know how to perform the basic operations of a code using the cyclical polynomial.
Be familiar with and know how to construct and work with algebraic code, Reed Solomon code and BCH code.
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Type B
|
Code |
Learning outcomes |
| B2 |
Know the basic notions of information theory and the meaning of the discipline.
Approach the noisy-channel coding theorem, and the problem of detection and correction of errors.
Have some idea of advanced concepts and advanced techniques in code theory: local decoding, list decoding, network coding, LDPC and iterative decoders, algebraic-geometric codes, etc.
Have some idea of other applications for codes (fingerprinting, steganography, cryptography, privacy, etc.).
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Type C
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Code |
Learning outcomes |
Topic |
Sub-topic |
Finite arithmetic and finite fields |
Divisibility, prime numbers, greatest common divisor.
Bézout's identity and Euclidean algorithm.
Congruences. Modular rings Zm.
Polynomials, polynomial divisibility, primitive elements.
Finite fields.
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Information coding (classical)
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Information theory. Noisy channels. Bloc codes. Hamming distance. Code length and correcting capability. Bounds.
Linear codes. Generator matrix and parity check matrix.
Error correction by syndrome.
Cyclic codes. Generator polynomial. Vandermonde matrices.
Algebraic codes. Reed-Solomon codes.
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Information coding (advanced) |
Ús de l'aritmètica modular en comunicacions digitals i en la criptografia. |
Methodologies :: Tests |
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Competences |
(*) Class hours
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Hours outside the classroom
|
(**) Total hours |
Introductory activities |
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1 |
0 |
1 |
Lecture |
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25 |
40 |
65 |
Problem solving, exercises in the classroom |
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15 |
20 |
35 |
Personal attention |
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1 |
0 |
1 |
PBL (Problem Based Learning) |
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12 |
18 |
30 |
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Practical tests |
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6 |
12 |
18 |
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(*) On e-learning, hours of virtual attendance of the teacher. (**) The information in the planning table is for guidance only and does not take into account the heterogeneity of the students. |
Methodologies
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Description |
Introductory activities |
Introductory activities |
Lecture |
Explanation of the contents |
Problem solving, exercises in the classroom |
At the beginning of the course a list of problems will be given to the students.
The problem solving classes are intended to be participative with active implication of the students. Problems will be solved collectively under the gudance of the professor.
|
Personal attention |
Personalized attention |
PBL (Problem Based Learning) |
A set of problems will be proposed in order to think and discuss about the learnt contents.
The discussions will be in small groups with the guidance of the professor and a formalized resolution will be required. |
Description |
The personalized attention will be used to solve doubts and questions of the students |
Methodologies |
Competences
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Description |
Weight |
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Practical tests |
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- Individual resolution of problems on arthmetics.
- Individual resolution of problems on vandermonde matrices and linear codes.
- Individual resolution of problems on cyclic codes and RS codes.
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33% cada uno, o 25% cada uno dependiendo de los otros parámetros |
Others |
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ABP assignments |
0% or 25% depending on the other parameters |
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Other comments and second exam session |
In all tests and exams, it is totally prohibited using or carrying communication devices. Tests are solved without calculator.Attendance at the labs is mandatory if the subject is taken for the first time. If it is not the first time that the subject is taken, the laboratory grade (ABP) of the previous year can be used.
The final mark is computed as follows: --- Individual resolution of problems 1 : PROB1 between 0 and 10 Individual resolution of problems 2 : PROB2 between 0 and 10 Individual resolution of problems 3 : PROB3 between 0 and 10. This mark has to be at least 3.5. --- Mark ABP 1 : ABP1 between 0 and 10 Mark ABP 2 : ABP2 between 0 and 10 Mark ABP 3 : ABP3 between 0 and 10 --- Mark ABP: (ABP1+ABP2+ABP3)/3, between 0 and 10 --- FINAL MARK FIRST CALL = MAX( (PROB1+PROB2+PROB3)/3, (PROB1+PROB2+PROB3+ABP)/4 ) FINAL MARK SECOND CALL = 100% of the final test |
Basic |
M. Bras-Amorós i O. Farràs Ventura, Matemàtica Discreta II, 2022, Universitat Rovira i Virgili
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Complementary |
R.M. Roth, Introduction to Coding Theory, 2006, Cambridge University Press
P. Garrett, The Mathematics of Coding Theory, 2003, Prentice Hall
N.L. Biggs , Discrete Mathematics , 2002, Oxford University Press
D. Applebaum , Probability and information : an integrated approach , 1996 , Cambridge University Press
F.J. MacWilliams, N.J.A. Sloane, The Theory of Error-Correcting Codes , 2006 , North-Holland
S. Roman , Coding and Information Theory , 1992, Graduate Texts in Mathematics
S. Xambó, Block Error-Correcting Codes, https://web.mat.upc.edu/sebastia.xambo/CC/CC-Book.html, Universitext, Springer, 2003
J.M. Brunat i E. Ventura, Informació i Codis, 2001, Universitat Politècnica de Catalunya
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Subjects that it is recommended to have taken before |
MATHEMATICAL ANALYSIS I/17234005 | LINEAR ALGEBRA/17234007 | DISCRETE MATHEMATICS I/17234009 |
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(*)The teaching guide is the document in which the URV publishes the information about all its courses. It is a public document and cannot be modified. Only in exceptional cases can it be revised by the competent agent or duly revised so that it is in line with current legislation. |
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