Combinatória e Teoria de Códigos (Coding Theory and Combinatorics) (Semestre 2 - 2018-2019)

 
Licenciatura em Matemática Aplicada e Computação e Mestrado em Matemática Aplicada



Docente: Pedro Martins Rodrigues - pmartins@math.tecnico.ulisboa.pt



Information and News        Program     Bibliography       Notes and Problems

Evaluation       Grades



Information and News

02/07 - The final exam will follow the same model of the tests: questions will be delivered next Monday, 08/07 and the answers must be handed back until Wednesday, 10/07. It is also possible to answer only the part of the exam corresponding to one of the tests; in this case the answers must be handed back until Tuesday, 09/07.To attend this exam it is mandatory to confirm the presence through Fenix until 4 p.m. of next Thursday, 04/07.

02/07 - The Grades of the Second Test have been really published. My apologies.

01/07 - Important: Each student is asked to write, as soon as possible, a message to let me know if she/he wants to attend the Final Exam.

01/07 - The Grades of the Second Test have been published, together with the resultant final grades.

01/07 - I apologize for the delay in the publication of the grades. I expect to update the Grades file later today or, in the worst case scenario, early tomorrow.

12/06 - The grades from the Homeworks have been published.

11/06 - Second Test: Each student is asked to send me, until next Friday, 14/06, a message confirming that she or he is willing to receive the questions from the second test in a message sent to the given e-mail adress, and to send back the answers in the same way. If necessary, a hard copy may be presented later.

The questions will be sent on Wednesday, 19/06, around 4 p.m., and the answers must be sent back until Friday, 21/06, at 10 a.m.

11/06 - Attending hours: I'll be available, from 10.00 to 12.00, on the 11/06, 12/06, 14/06 and 17/06. Other attending hours may be possible, if requested.

07/06 - A first version of Notes IX has been published.

28/05 - Due to a medical appointment, which is impossible to postpone, there will be no class next Friday, 31/05. The supplementary class will take place Thursday, 06/06, at 10 a.m. in room V1.16.

22/05 - Notes VIII has been published.

17/05 - Homework: Exercises 19 and 20 from Notes VII must be delivered until next Friday, 24/05, in class.

17/05 - Notes VII has been published.

14/05 - A new update of Notes II was published.

11/05 - Homework: Exercises 9 and 10 from Notes VI must be delivered until next Friday, 17/05, in class.

11/05 - Notes VI has been published. Notes II were updated (a new update will be published soon).

10/05 - The grades of Test 1 were published.

30/04 - A file Notes III (Information Theory and Coding) has been published.

02/04 - The supplementary class will take place on 09/04, at 4 p.m., in room V1.33.

29/03 - A first version of Notes V has been published. The Homework assignement to be delivered until 05/04, in class, consists of the following problems: Notes V - problems 44 and 45.

21/03 - The file Notes IV was updated. The Homework assignement to be delivered until 29/03, in class, consists of the following problems: Notes IV- problem 50, problem 53 a) and c), problem 55.

18/03 - The file Notes IV about Finite fields has been published.

14/03 - Notes I and II were updated.

12/03 - The statement of problem 47 from Notes II was modified.

11/03 - Attending Hours I'll be available in my office every Tuesday from 10 to 12.

06/03 - The Homework assignement to be delivered until 14/03, in class, consists of the following problems: Notes I - Problem 27, Problem 29 b) and c). Notes II- Proof of proposition 24, Problem 42, Problem 44 and Problem 47.

06/03 - The file Notes II has been published.

04/03 - An error in exercise 32 d) from Notes I was corrected. The publication of Notes II had to be delayed, hopefully until tomorrow.

22/02 - The file Notes I has been published.

19/02 - A short (and tentative) plan for the lectures has been published.

12/02 - Information and materials for the course will be made available in this page. The information concerning the program and bibliography contained below is incomplete and will be updated later.

The following annoucement was already published in the Fenix webpage:

Classes for the course on Coding Theory and Combinatorics will start next week.

All students planning to attend the course, or that may be interested in doing so, are invited to visit me at my office for a short conversation; these are intended to give me some information about each student mathematical background and previous knowledge of the subject and, of course, to answer any questions that the students may want to ask. I'll be available on 14/02, 18/02 and 19/02, from 9.30 to 12.00, but I would appreciate a message announcing your visit.



Program

Matemática Discreta Enumerativa: Princípio de inclusão-exclusão. Funções geradoras. Relações de recorrência. Teoria de Códigos: O problema principal da Teoria de Códigos. Corpos finitos e espaços vectoriais sobre corpos finitos. Códigos lineares. Códigos cíclicos.




Bibliography

A Course in Error-Correcting Codes, J. Justensen & T. Høholdt, EMS Textbooks in Mathematics, 2017.

Coding Theory, a First Course, San Ling & Chaoping Xing, Cambridge University Press, 2004.

Fundamentals of Error-Correcting Codes, W. Cary Huffman & Vera Pless, Cambridge University Press, 2003.

Coding and Information Theory, Steven Roman, Springer-Verlag, 1992.

Notes and Problems

Plan for Lectures

Notes I       Notes II

Notes III

Notes IV       Notes V

Notes VI       Notes VII

      Notes VIII

Notes IX



Evaluation
The main evaluation consists of two tests (11/04 and 19/06, 90 minutes each) with the option of a final exam (05/07, 3 hours), supplemented by homework assignments. Students attending the tests may also attend the exam.

The final grade, in a scale 0-20, will be given by max(max(Tests, Exam), 0.8 max(Tests, Exam)+0.2 Homework).



Grades

HomeWork Grades      Grades