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Week
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Topics
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Study Metarials
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1
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Polynomials and words
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R1- Chapter 4.1
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2
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Introduction to cyclic codes
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R1- Chapter 4.2
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3
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Generating and parity check matrices for cyclic codes
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R1- Chapter 4.3
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4
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Finding cyclic codes; dual cyclic codes
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R1- Chapter 4.4, Chapter 4.5
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5
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Finite fields
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R1- Chapter 5.1
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6
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Minimal polynomials
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R1- Chapter 5.2
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7
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Cyclic Hamming codes; BCH codes; decoding two error-correcting BCH codes
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R1- Chapter 5.3, Chapter 5.4, Chapter 5.5
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8
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Codes over GF(2^r); Reed-Solomon codes
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R1- Chapter 6.1, Chapter 6.2
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9
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Decoding Reed-Solomon codes
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R1- Chapter 6.3
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10
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Transform approach to Reed-Solomon codes
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R1- Chapter 6.4
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11
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Berlekamp-Massey algorithm; erasures
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R1- Chapter 6.5, Chapter 6.6
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12
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Burst error-correcting codes
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R1- Chapter 7.1
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13
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Interleaving
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R1- Chapter 7.2
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14
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Application to compact discs
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R1- Chapter 7.3
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Prerequisites
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-
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Language of Instruction
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English
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Responsible
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Asst. Prof. Dr. Celalettin KAYA
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Instructors
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-
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Assistants
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-
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Resources
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R1- Hankerson D. R., Hoffman D: G., Leonard D. A., Lindler C. C., Phelps K. T., Rodger C. A., Wall J. R. (2000). Coding Theory and Cryptography: The Essentials (Second Edition, Revised and Expanded). Marcel Dekker, New York.
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Supplementary Book
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SR1- Bierbrauer J. (2005). Introduction to Coding Theory. Chapman & Hall / CRC, Boca Raton.
SR2- Roman S. (1997). Introduction to Coding and Information Theory (Undergraduate Texts in Mathematics). Springer-Verlag, New York.
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Goals
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To introduce basic notions about cyclic linear codes, and to teach BCH codes, Reed-Solomon codes and burst error-correcting codes.
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Content
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Cyclic codes; Finite fields; Cyclic Hamming codes, BCH codes, Reed-Solomon codes, Burst error-correcting codes; Berlekamp-Massey algorithm.
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Program Learning Outcomes |
Level of Contribution |
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1
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Having advanced theoretical and applied knowledge in the basic areas of mathematics
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3
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2
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Ability of abstract thinking
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2
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3
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To be able to use the acquired mathematical knowledge in the process of defining, analyzing and separating the problem encountered into solution stages.
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3
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4
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Associating mathematical achievements with different disciplines and applying them in real life
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2
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5
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Ability to work independently in a problem or project that requires knowledge of mathematics
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-
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6
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Ability to work harmoniously and effectively in national or international teams and take responsibility
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-
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7
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Having the skills to critically evaluate and advance the knowledge gained from different areas of mathematics
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-
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8
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To be able to determine what kind of knowledge learning the problem faced and to direct this knowledge learning process.
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-
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9
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To adopt the necessity of learning constantly by observing the improvement of scientific accumulation over time
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-
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10
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Ability to verbally and in writing convey thoughts on mathematical issues, and solution proposals to problems, to experts or non-experts.
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-
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11
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Being able to produce projects and organize events with social responsibility awareness
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-
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12
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Being able to follow publications in the field of mathematics and exchange information with colleagues by using a foreign language at least at the European Language Portfolio B1 General Level
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-
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13
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Ability to use computer software (at least at the Advanced Level of European Computer Use License), information and communication technologies for solving mathematical problems, transferring ideas and results
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-
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14
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Being conscious of acting in accordance with social, scientific, cultural and ethical values
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-
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