Binary-ternary mixed code

Binary-ternary mixed code[1]

Description

Encodes \(K\) states (codewords) in a string of \(n_1+n_2\) coordinates, with the first \(n_1\) coordinates being binary, and the last \(n_2\) coordinates being ternary.

Protection

See Ref. [2,3] for bounds on binary-ternary mixed codes.

Notes

Binary-ternary mixed codes have been used in football pools, in which \(n_1\) of the matches result in either a win, a loss, or a draw, but \(n_2\) of the matches are assumed to have only a win or a loss outcome [1].

Parent

Mixed code

Cousin

Covering code — See Ref. [4] for bounds on binary-ternary mixed covering codes.

References

[1]: H. Hämäläinen and S. Rankinen, “Upper bounds for football pool problems and mixed covering codes”, Journal of Combinatorial Theory, Series A 56, 84 (1991) DOI
[2]: A. E. Brouwer, H. O. Hamalainen, P. R. J. Ostergard, and N. J. A. Sloane, “Bounds on mixed binary/ternary codes”, IEEE Transactions on Information Theory 44, 140 (1998) DOI
[3]: B. Litjens, “Semidefinite bounds for mixed binary/ternary codes”, Discrete Mathematics 341, 1740 (2018) arXiv:1606.06930 DOI
[4]: J. H. van Lint Jr. and G. J. M. van Wee, “Generalized bounds on binary/ternary mixed packing and covering codes”, Journal of Combinatorial Theory, Series A 57, 130 (1991) DOI

Page edit log

Victor V. Albert (2024-02-08) — most recent

Cite as:

“Binary-ternary mixed code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/binary-ternary

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/groups/mixed/binary-ternary.yml.