Mathematical Coding

Mathematical Coding#

Table of Contents#

Sections#

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.

more

  • [ y ] 11-23-2023. Primal Space. “Voyager’s 15 Billion Mile Software Update”.

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 Error Rate

  • [ 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 ] Cyclic Redundancy Check (CRC)

  • [ w ] Cyclic Redundancy Check, Computation

  • [ 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 ] Low-Density Parity-Check (LDPC) 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

Contents