Mixed code

Description

Encodes \(K\) states (codewords) in a string of coordinates which takes values in more than one group.

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 caled 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 Unpublished manuscript, Queen Mary and Westfield College, London (1998).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