---
title: "Notes on Digital Coding"
authors:
  - "Marcel J. E. Golay"
year: 1949
venue: "Proceedings of the IRE"
arxiv: null
doi: "10.1109/JRPROC.1949.233620"
source: "https://doi.org/10.1109/JRPROC.1949.233620"
topics:
  - golay-code
  - coding-theory
  - error-correcting
seed_rank: 569
seed_batch: "foundations-greats-2026-08-13"
reviewed: "2026-08-13"
pool: "systems"
relevance_score: 8
lineage: foundations-of-computing
cites:
  - title: "Error Detecting and Error Correcting Codes"
    url: "https://doi.org/10.1002/j.1538-7305.1950.tb00463.x"
    year: 1950
    arxiv: null
    doi: "10.1002/j.1538-7305.1950.tb00463.x"
  - title: "A Mathematical Theory of Communication"
    url: "https://doi.org/10.1002/j.1538-7305.1948.tb01338.x"
    year: 1948
    arxiv: null
    doi: "10.1002/j.1538-7305.1948.tb01338.x"
see:
  - "568-error-detecting-and-error-correcting-codes"
  - "553-a-mathematical-theory-of-communication"
---

# Notes on Digital Coding

## One-sentence takeaway

Golay's half-page IRE note announces the perfect binary \((23,12)\) and ternary \((11,6)\) codes that later bear his name.

## Why it matters here

Perfect codes are existence miracles in the same packing geometry Hamming uses; Broadside reliability lore needs both cards.

## Key ideas

- A perfect code saturates the Hamming (sphere-packing) bound: spheres of radius \(t\) around codewords partition the space.
- The binary Golay code has length 23, dimension 12, minimum distance 7 (triple-error-correcting).
- The ternary Golay code is the \((11,6,5)\) companion.
- The note is a correspondence, not a development; the constructions were unpacked by later coding theory.
- Dated 1949, it slightly precedes Hamming's 1950 BSTJ paper in print.

## Caveats

## Links

- DOI: [10.1109/JRPROC.1949.233620](https://doi.org/10.1109/JRPROC.1949.233620)
- URL: https://doi.org/10.1109/JRPROC.1949.233620