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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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“ble scalar). Note that therefore gcd(Λ,Ω) = 1 as the elements of E are all the zeroes of Λ but definitely not zeroes of Ω. The three defined polynomials are related by the famous Key Equation (see e.g. [19] or [28]): Λ(x)S(x) ≡ Ω(x) mod xd−1 (4) Many decoding algorithms solve this equation for Λ and Ω, and construct c f…”
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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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