Description
Codebook that shortens a telegram by mapping each word, phrase, or sentence to a five-letter codeword [1; Secs. 1 and 3]. Later telegraph codes required any two codewords to differ in at least two letters, so that a single mutilated letter yields a string outside the codebook [1; Sec. 3].
Telegraph codes with a two-letter difference are \((5,K,2)_{26}\) codes over the Latin alphabet in the Hamming metric [1; Sec. 3]. Telegraph codes generalize to codebooks whose codewords have mixed lengths, as in early codebooks [2][1; Sec. 3]. In the 1937 New Boe Code, the middle letter of each codeword is fixed by its first two and last two letters, as listed in a mutilation table [1; Sec. 3].
Protection
A three-letter difference allows single-letter errors to be corrected [1; Sec. 3]. In addition to a two-letter difference, the 1923 Acme Commodity and Phrase Code aimed to detect transpositions of adjacent letters, but pairs such as HALAN and HAALN escape detection [1; Fig. 8]. Telegraph codes were designed against the errors of their transmission medium [1; Secs. 3 and 6]. These include dropped dots or dashes and split letters in Morse code, and transpositions and adjacent-keystroke errors on teletypes [1; Secs. 3 and 6].Decoding
Mutilation-table lookup lists the candidate codewords for a received non-codeword, e.g., five for ZNBAB, and the meaning of the decoded text is used to select one [1; Sec. 3].Terminal indices list codewords alphabetized by their last two letters, for use when the beginning of a codeword is corrupted [1; Sec. 3].Realizations
Commercial telegraphy: the 1920 A B C Telegraphic Code, Sixth Edition, used a two-letter difference, as did the 1923 Acme Commodity and Phrase Code with \(K=100\,000\) codewords [1; Sec. 3].Astronomical telegrams: the 1888 Science Observer Code encodes numbers below 40000 as mixed-length words of up to ten letters, pairwise at least two letters apart [3]. A control word equal to a quarter of the sum of the preceding numbers lets the receiver recompute one mutilated number [3].Notes
Telegraph codes used a minimum letter difference between codewords several decades before Hamming distance was formalized [1; Sec. 3].See Ref. [4] for an analysis of how the two-letter difference and vowel-density requirements reduce the number of available codewords.Encryption schemes for telegraph codes mapped codewords to codewords, since a generic cipher would destroy properties such as the two-letter difference [1; Sec. 3].Cousin
- Checksum code— Telegraph codes protected numerical data with check digits or letters, which act as checksums over the plaintext and were usually computed modulo 10 [1; Sec. 3].
Primary Hierarchy
References
- [1]
S. M. Bellovin, “Compression, correction, confidentiality, and comprehension: a modern look at telegraph codebooks”, Cryptologia 50, 374 (2025) DOI
- [2]
A. Barg, “At the Dawn of the Theory of Codes”, The Mathematical Intelligencer 15, 20 (1993) DOI
- [3]
S. C. Chandler, Jr. and J. Ritchie, Jr., The Science Observer Code (Boston Scientific Society, 1888) URL
- [4]
W. F. Friedman and C. J. Mendelsohn, “Notes on Code Words”, The American Mathematical Monthly 39, 394 (1932) DOI
Page edit log
- Victor V. Albert (2026-11-11) — most recent
- Victor V. Albert (2026-10-29)
Cite as:
“Telegraph code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/telegraph, arXiv:2606.11484