Error Detecting and Error Correcting Codes.

Hamming, R. W. (1950). Error Detecting and Error Correcting Codes. Bell System Technical Journal, 29(2), 147-160.

Type

Journal article

Intellectual base

Primary research

Year

1950

Volume

29

Issue

2

Pages

147-160

ISSN

1538-7305

DOI

10.1002/j.1538-7305.1950.tb00463.x

DOI registrant

Institute of Electrical and Electronics Engineers

Link

https://doi.org/10.1002/j.1538-7305.1950.tb00463.x

Cited from

computer_science, engineering_design, information_theory, mathematics, physics, statistics_experimental_design, systems_cybernetics

Cited by

9 citations across 9 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Compression

  • This sourceFoundational error-control coding (Hamming codes/distance). DOI verified.

• Data Integrity
  • The specified threat model (accidental corruption, concurrent modification, malicious tampering, operator error)

    This sourceIntroduces single-error-correcting / double-error-detecting codes (Hamming codes) and minimum-distance theory.

    Supported in partVerified against the publisher's abstract

    Hamming's abstract treats undetected machine error as catastrophic, backing only the accidental-corruption element of the stated four-part threat model, not concurrent modification, tampering, or operator error.

    “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.”

    Read by an automated reader; not a human review. How support was checked

• Discrete vs. Continuous (Quantization)

  • This sourceIntroduces Hamming codes for detecting and correcting errors in discrete data.

• Measurement Uncertainty and Observational Noise
  • Listed in the references but not attached to a specific claim.
• Metric
  • In information theory and coding it is Hamming distance between binary strings, edit distance between texts, and Levenshtein distance for sequence alignment.

    This sourceIntroduces the Hamming distance between binary strings as a metric for coding theory; Levenshtein (1966) extends to edit distance.

• Multiplexing
  • Listed in the references but not attached to a specific claim.
• Redundancy
  • The probability of simultaneous independent failure of N components shrinks exponentially in N under independence, the load-bearing mathematical property enabling reliability levels (5, 6, 9 nines of uptime) that no single component achieves

    This sourceHamming exponential failure probability independence.

• Signal Decay and Fadeout
  • Listed in the references but not attached to a specific claim.

Mechanisms

• Redundancy-Based Error Detection
  • Spend redundancy on detection or correction. A minimal code (single parity bit) only flags that something is wrong; a richer code with greater minimum distance can also pinpoint which symbols are wrong and flip them back.

    This sourceShows that parity can detect an error without locating it, while codes with sufficient minimum distance can locate and correct corrupted symbols.

Verification

Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.

Does it back the claim? Read against the text for 1 of 9 citations: 1 supported in part. Each verdict is shown under its citation below, with what in the work backs the sentence.

Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.

See how references were verified.

Registry ID ref:479ff733e83f · see in the full table