Error Detecting and Error Correcting Codes
Open accessAbstract
The author was led to the study given in this paper from a consideration of large scale computing machines in which a large number of operations must be performed without a single error in the end result. This problem of “doing things right” on a large scale is not essentially new; in a telephone central office, for example, a very large number of operations are performed while the errors leading to wrong numbers are kept well under control, though they have not been completely eliminated. This has been achieved, in part, through the use of self-checking circuits. The occasional failure that escapes routine checking is still detected by the customer and will, if it persists, result in customer complaint, while if it is transient it will produce only occasional wrong numbers. At the same time the rest of the central office functions satisfactorily. In a digital computer, on the other hand, a single failure usually means the complete failure, in the sense that if it is detected no more computing can be done until the failure is located and corrected, while if it escapes detection then it invalidates all subsequent operations of the machine. Put in other words, in a telephone central office there are a number of parallel paths which are more or less independent of each other; in a digital machine there is usually a single long path which passes through the same piece of equipment many, many times before the answer is obtained.
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“Since R ( M, D ) , R ( M, D S ) , and R ( M D , D S ) are binary vectors, we use the normalized Hamming distance (Hamming, 1950): With a benchmark dataset D and a LLM M , we define the fidelity and resistance metrics for strategy S as: Discussion.”
- Authors
- Hamming, R. W.
- Corresponding author
- Hamming, R. W.
- Venue
- Bell System Technical Journal
- Published
- 1950-04
- Volume
- 29
- Issue
- 2
- Pages
- 147-160
- ISSN
- 0005-8580 (ISSN-L)
- OpenAlex
- W1980073965
- Cited by
- 5,377
- References
- 0
- Citations by year
- 2026: 195 · 2025: 297 · 2024: 267 · 2023: 249 · 2022: 240 · 2021: 263 · 2020: 281 · 2019: 294 · 2018: 253 · 2017: 272 · 2016: 244 · 2015: 260 · 2014: 243 · 2013: 281 · 2012: 207
- FWCI
- 8.06
- Type
- journal article
- Language
- en
- Open access
- green
- hdl.handle.net
- Locations
- Bell System Technical Journal (publishedVersion)
- Calhoun: The Naval Postgraduate School Institutional Archive (Naval Postgraduate School) (submittedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Coding theory and cryptography
- Physical Sciences › Computer Science › Computer Networks and Communications › Error Correcting Code Techniques
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Radiation Effects in Electronics
- Keywords
- error detection codes, error-correcting codes, digital computers, self-checking circuits, fault tolerance, transient faults, telephone central offices
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