Mathematical Coding Theory

Resources

Ben Eater

• [ y ] Ben Eater. (2020). "What is error correction? Hamming codes in hardware". YouTube.
• [ y ] Ben Eater. (2018). "Error detection: Parity checking". YouTube.
• [ y ] Ben Eater. (2018). "Reliable data transmission". YouTube.

3Blue1Brown

• [ y ] Grant Sanderson. (2020). "Hamming codes and error correction". YouTube.
• [ y ] Grant Sanderson. (2020). "Hamming codes part 2, the elegance of it all". YouTube.

Figures

• [ w ] Hamming, Richard (1915-1998)
• [ w ] Shannon, Claude (1916-2001)

Texts

• Ball, Simeon. (2020). A Course in Algebraic Error-Correcting Codes.
• Berlekamp, Elwyn R. (2015). Algebraic Coding Theory.
• Bierbrauer, Jurgen. (2016). Introduction to Coding Theory.
• Biggs, Norman L. Codes: An Introduction to Information Communication and Cryptography. Springer Undergraduate Mathematics Series.
• Blahut, Richard E. (2003). Algebraic Codes for Data Transmission. Cambridge University Press.
• Brzezinski, Juliusz. (2018). Galois Theory Through Exercises. Springer.
• Csiszár, Imre & János Körner. (2011). Information Theory: Coding Theorems for Discrete Memoryless Systems. Cambridge University Press.
• Golomb, Solomon W., Robert E. Peile, & Robert A. Scholtz. (1994). Basic Concepts in Information Theory and Coding: The Adventures of Secret Agent 00111. Springer.
• Hamming, Richard W. (1985). Coding and Information Theory.
• Hill, Raymond. (1990). A First Course in Coding Theory. Clarendon Press: Oxford Applied Mathematics and Computing Science Series.
• Huffman, W. Cary. & Vera Pless. (2010). Fundamentals of Error-Correcting Codes. Cambridge University Press.
• Humphreys, J. F. & M. Y. Prest. (2004). Numbers, Groups, and Codes, 2nd Ed. Cambridge University Press.
• Jones, Gareth A. & J. Mary Jones. (2000) Information and Coding Theory. Springer Undergraduate Mathematics Series.
• MacWilliams, F. J. & N. J. A. Sloane. (1977). The Theory of Error-Correcting Codes.
• Moon, Todd K. (2021). Error Correction Coding: Mathematical Methods and Algorithms. Wiley.
• Moser, Stefan M. & Po-Ning Chen. (2012). A Student's Guide to Coding and Information Theory. Cambridge University Press.
• Neubauer, Andre. (2007). Coding Theory: Algorithms, Architectures, and Applications. Wiley.
• Peterson, W. Wesley. (1972). Error-Correcting Codes. 2nd Ed. MIT Press.
• Pierce, John R. (1980). An Introduction to Information Theory: Symbols, Signals, and Noise. Dover.
• Pretzel, Oliver. (1992). Error-Correcting Codes and Finite Fields. Oxford University Press Applied Mathematics and Computing Science Series.
• Reza, Fazlollah M. (1994). An Introduction to Information Theory. Dover.
• Roman, Steven. (1997). Introduction to Coding and Information Theory. Springer Undergraduate Texts in Mathematics.
• Roman, Steven. (1992). Coding and Information Theory. Springer Graduate Texts in Mathematics.
• Roth, Ron. (2006). Introduction to Coding Theory. Cambridge University Press.
• Sanvicente, Emilio. (2019). Understanding Error Control Coding. Springer.
• Stepanov, Serguei A. (1999). Codes on Algebraic Curves. Springer.
• Sweeney, Peter. (2002). Error Control Coding: From Theory to Practice. Wiley.
• Tomlinson et al. (2017). Error-Correction and Decoding: Bounds, Codes, Decoders, Analysis, and Applications. Springer Signals and Communication Technology.
• Trappe, Wade & Lawrence Washington. (2005). Introduction to Cryptography with Coding Theory. Pearson.
• Van Lint, J. H. (1999). Introduction to Coding Theory, 3rd Ed. Springer Graduate Texts in Mathematics.

Terms

• [ w ] BCH Code
• [ w ] Binary Code
• [ w ] Bit Rate
• [ w ] Bit Rate Reduction
• [ w ] Block Code
• [ w ] Channel Capacity
• [ w ] Channel Coding
• [ w ] Code
• [ w ] Code Rate
• [ w ] Codeword
• [ w ] Coding Theory
• [ w ] Convolutional Code
• [ w ] Cryptography
• [ w ] Cyclic Code
• [ w ] CRC Cyclic Redundancy Check
• [ w ] Data Compression
• [ w ] Decoding
• [ w ] Error Detection and Correction
• [ w ] Error-Correcting Code (ECC)
• [ w ] FEC Forward Error Correction
• [ w ] Golay Code
• [ w ] Goppa Code
• [ w ] Hadamard Code
• [ w ] Hamming Code
• [ w ] Hamming Distance
• [ w ] Information Rate
• [ w ] Information Theory
• [ w ] Line Code
• [ w ] Linear Code
• [ w ] Maximum Likelihood Decoding
• [ w ] Minimum Distance Decoding
• [ w ] Noisy-Channel Coding Theorem
• [ w ] Noisy Channel Model
• [ w ] Parity Bit
• [ w ] Perfect Code
• [ w ] Plotkin Bound
• [ w ] Polar Code
• [ w ] Polynomial Code
• [ w ] Reed-Muller Code
• [ w ] Reed-Solomon Code
• [ w ] Repetition Code
• [ w ] Shannon's Theorem
• [ w ] Source Coding
• [ w ] Syndrome Decoding