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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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“al proof for these facts in terms of the generated syndromes. To summarize the parameters of the construction we need the parameters of t-error-correcting codes of lengthb. We can use BCH codes [13], [15] for this purpose. If ℓ is the least integer such that b ≤ 2ℓ − 1 then there exists a t-errorcorrecting BCH code of…”
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“, [41]).”
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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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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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