Mixed code

Also known as Mixed-alphabet code.

Description

Encodes \(K\) states (codewords) in a string of two or more coordinates, each of which takes values in one of two or more possible groups.

The Hamming, Singleton, and Plotkin bounds are straightforwardly extended to mixed alphabets [1; Thm. 5.1].

Orthogonal array (OA) — Orthogonal arrays generalized to mixed alphabets are called mixed-level orthogonal arrays [2,3], (see [4; Ch. 9]). See Ref. [5] for bounds on mixed orthogonal arrays.
Combinatorial design — Combinatorial designs have been generalized to mixed alphabets [6].

[1]: Cameron, Peter J. "Some bridges between codes and designs." Unpublished manuscript, Queen Mary and Westfield College, London (1998).
[2]: Addelman, S., & Kempthorne, O. (1961b). Orthogonal Main-Effect Plans. Technical Report ARL 79, Aeronautical Research Lab., Wright-Patterson Air Force Base, Ohio, Nov. 1961.
[3]: C. R. RAO, “Some Combinatorial Problems of Arrays and Applications to Design of Experiments††Paper read at the International Symposium on Combinatorial Mathematics and its Applications, Fort Collins, Colorado, September 1971.”, A Survey of Combinatorial Theory 349 (1973) DOI
[4]: A. S. Hedayat, N. J. A. Sloane, and J. Stufken, Orthogonal Arrays (Springer New York, 1999) DOI
[5]: N. J. A. Sloane and J. Stufken, “A linear programming bound for orthogonal arrays with mixed levels”, Journal of Statistical Planning and Inference 56, 295 (1996) DOI
[6]: W. J. Martin, Designs, Codes and Cryptography 16, 271 (1999) DOI

Page edit log

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