# 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

## 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 two of the three possible outcomes [1].

## Parent

## 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 et al., “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