Two-in-five code

Two-in-five code[1]

Alternative names: Two-out-of-five code.

Description

A nonlinear binary code consisting of the 10 weight-two five-bit strings, thereby providing an encoding for the decimal digits 0 through 9.

Protection

Detects some single bit-flips as well as unidirectional errors using the fact that each codeword has weight two. The code fails for any sequence of flips that maintains the constant weight.

Realizations

Used in the United States Postal Service’s POSTNET barcode system as well as the Postal Alpha-numeric Encoding Technique (PLANET).Forms the numerical part of the Code 39 barcode encoding.Early IBM computers [2,3].

Member of code lists

Primary Hierarchy

Classical Domain

Binary Kingdom

Binary codeECC

Binary group-orbit codeECC

Parents

Binary group-orbit code

The two-in-five code is a binary group-orbit code with group \(S_5\).

Weight-two codeConstant-weight ECC

Two-in-five code

References

[1]: R. W. Hamming, Letter, April 5, 1978.
[2]: J. Svigals, “IBM 7070 data processing system”, Papers presented at the the March 3-5, 1959, western joint computer conference on XX - IRE-AIEE-ACM ’59 (Western) 222 (1959) DOI
[3]: T. Thompson, From Error-Correcting Codes Through Sphere Packings to Simple Groups (American Mathematical Society, 1983) DOI

Page edit log

Victor V. Albert (2022-08-12) — most recent

Cite as:

“Two-in-five code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/two_in_five

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/bits/constant_weight/two_in_five.yml.