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Introduction to Coding Theory
Abstract
Error-correcting codes constitute one of the key ingredients in achieving the high degree of reliability required in modern data transmission and storage systems. This 2006 book introduces the reader to the theoretical foundations of error-correcting codes, with an emphasis on Reed-Solomon codes and their derivative codes. After reviewing linear codes and finite fields, the author describes Reed-Solomon codes and various decoding algorithms. Cyclic codes are presented, as are MDS codes, graph codes, and codes in the Lee metric. Concatenated, trellis, and convolutional codes are also discussed in detail. Homework exercises introduce additional concepts such as Reed-Muller codes, and burst error correction. The end-of-chapter notes often deal with algorithmic issues, such as the time complexity of computational problems. While mathematical rigor is maintained, the text is designed to be accessible to a broad readership, including students of computer science, electrical engineering, and mathematics, from senior-undergraduate to graduate level.
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“For example, the Reed–Solomon code can correct up to e erasures and s substitutions with 2s + e additional symbols.”
From Emerging Approaches to DNA Data Storage: Challenges and Prospects (2022) · cites this paper as [90]
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Items 901–923 of 923
Quasi-cyclic binary extended and expurgated Goppa codes and their parameters
Li, F., Jia, X., Sun, H., et al. (2026) · Designs Codes and Cryptography · doi:10.1007/s10623-025-01797-4
Generalized hyperderivative Reed–Solomon codes
Can, M. B., & Horowitz, B. (2026) · Designs Codes and Cryptography · doi:10.1007/s10623-026-01849-3
Cyclotomic Classes in a Product of Finite Abelian Groups and Applications
Jitman, S. (2026) · Journal of Mathematics · doi:10.1155/jom/1381907
Diversity Transforms for OTFS-Based LEO Nonterrestrial Networks
Basnayaka, C. M. W., Lee, H., Sooriarachchi, V. P., et al. (2026) · IEEE Internet of Things Journal · doi:10.1109/jiot.2026.3702433
Wang, C., Sima, J., & Raviv, N. (2026) · IEEE Transactions on Information Theory · doi:10.1109/tit.2026.3708787
Decoding and List Decoding Algorithms for Generalized Roth-Lempel Codes
Sun, H., Li, F., Jia, X., et al. (2026) · IEEE Transactions on Information Theory · doi:10.1109/tit.2026.3710202
Concatenated error-correcting codes for the interference channel with multi-antenna reception
Tang, Y., & Sidiropoulos, N. D. (2026) · International Conference on Communications · doi:10.1109/icc59461.2026.11586780
New Upper Bounds for Binary Linear Covering Codes
Davydov, A. A., Marcugini, S., & Pambianco, F. (2026) · IEEE Transactions on Information Theory · doi:10.1109/tit.2026.3716379
Robust Trace-Repair for Full-Length Reed–Solomon Codes
Kim, W., Kruglik, S., Luo, G., et al. (2026) · IEEE Transactions on Communications · doi:10.1109/tcomm.2026.3716997
BCH and RS Codes for DNA Data Storage
Arslan, S. S. (2026) · Springer eBooks · doi:10.1007/978-981-95-9450-4_6
HBM-CASO: A Coordinated Approach to HBM System-Level and On-Die ECC
Zhu, R., Guo, Y., Li, H., et al. (2026) · ACM/IEEE International Symposium on Computer Architecture (ISCA) · doi:10.1109/isca66397.2026.00026
Duangpan, A., Boonklurb, R., & Sutthimat, P. (2026) · Mathematics · doi:10.3390/math14162866
Adaptive Symmetric Private Linear Computation from Repairing Reed-Solomon Codes
Wang, T., Shi, Z., Deng, L., et al. (2026) · IEEE International Symposium on Information Theory (ISIT) · doi:10.1109/isit62367.2026.11653700
Efficient 0-insertion/deletion error control codes based on Reed-Solomon codes
Tallin, L. G., & Bose, B. (2026) · IEEE International Symposium on Information Theory (ISIT) · doi:10.1109/isit62367.2026.11653991
Liu, L., Yu, J.-H., Wu, W.-J., et al. (2026) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2026.3724255
Application: Optimal Decoding in Communications Engineering
Schäffler, S. (2012) · Springer series in operations research/Springer series in operations research and financial engineering · doi:10.1007/978-1-4614-3927-1_4
Mathematical optimisation and signal processing techniques in wireless relay networks
Krishna, R. (2009) · Loughborough University Institutional Repository (Loughborough University)
Distributed Computation Using Algebraic Elements
Matthysse, S. (1987) · Springer eBooks · doi:10.1007/978-94-009-3833-5_21
Metadata
- Authors
- Roth, R.
- Affiliations
- Technion – Israel Institute of Technology (IL)
- Corresponding author
- Roth, Ron
- ORCID
- Roth, Ron
- Venue
- Cambridge University Press eBooks
- Publisher
- Cambridge University Press
- Published
- 2006-02-23
- OpenAlex
- W2895239415
- Cited by
- 912
- References
- 0
- Citations by year
- 2026: 21 · 2025: 31 · 2024: 45 · 2023: 40 · 2022: 30 · 2021: 46 · 2020: 55 · 2019: 53 · 2018: 65 · 2017: 46 · 2016: 42 · 2015: 52 · 2014: 41 · 2013: 54 · 2012: 67
- FWCI
- 11.57
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- Cambridge University Press eBooks (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Coding theory and cryptography
- Physical Sciences › Computer Science › Computer Networks and Communications › Error Correcting Code Techniques
- Physical Sciences › Computer Science › Computer Networks and Communications › Advanced Data Storage Technologies
- Keywords
- error-correcting codes, Reed-Solomon codes, linear codes, finite fields, cyclic codes, MDS codes, graph codes, concatenated codes, trellis codes, convolutional codes, Reed-Muller codes, burst error correction, decoding algorithms, data transmission reliability, data storage reliability
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