Orthogonal array (OA)[13] 

Description

An orthogonal array, or OA\(_{\lambda}(t,n,q)\), of strength \(t\) with \(q\) levels and \(n\) constraints is a set of \(q\)-ary strings such that any subset of \(t\) coordinates contains every length-\(t\) string an equal number of times \(\lambda\), which is the index of the array.

Notes

See [4] for a book on orthogonal arrays.

Parents

Children

Cousins

References

[1]
C. R. Rao, Hypercubes of strength d leading to confounded designs in factorial experiments. Bull. Calcutta Math. Soc., 38, 67-78.
[2]
C. R. Rao, “Factorial Experiments Derivable from Combinatorial Arrangements of Arrays”, Supplement to the Journal of the Royal Statistical Society 9, 128 (1947) DOI
[3]
C. R. Rao, “On a Class of Arrangements”, Proceedings of the Edinburgh Mathematical Society 8, 119 (1949) DOI
[4]
A. S. Hedayat, N. J. A. Sloane, and J. Stufken, Orthogonal Arrays (Springer New York, 1999) DOI
[5]
Delsarte, Philippe. "An algebraic approach to the association schemes of coding theory." Philips Res. Rep. Suppl. 10 (1973): vi+-97.
[6]
Ph. Delsarte, “Hahn Polynomials, Discrete Harmonics, andt-Designs”, SIAM Journal on Applied Mathematics 34, 157 (1978) DOI
[7]
V. I. Levenshtein, “Universal bounds for codes and designs,” in Handbook of Coding Theory 1, eds. V. S. Pless and W. C. Huffman. Amsterdam: Elsevier, 1998, pp.499-648.
[8]
P. Delsarte and V. I. Levenshtein, “Association schemes and coding theory”, IEEE Transactions on Information Theory 44, 2477 (1998) DOI
[9]
G. Kuperberg, S. Lovett, and R. Peled, “Probabilistic existence of regular combinatorial structures”, (2017) arXiv:1302.4295
[10]
P. Delsarte, “Four fundamental parameters of a code and their combinatorial significance”, Information and Control 23, 407 (1973) DOI
[11]
T. Etzion and A. Vardy, “Perfect binary codes: constructions, properties, and enumeration”, IEEE Transactions on Information Theory 40, 754 (1994) DOI
[12]
P. R. J. Ostergard, O. Pottonen, and K. T. Phelps, “The Perfect Binary One-Error-Correcting Codes of Length 15: Part II—Properties”, IEEE Transactions on Information Theory 56, 2571 (2010) arXiv:0903.2749 DOI
[13]
P. R. J. Östergård, "Construction and Classification of Codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI
[14]
Delsarte, Philippe. "Bounds for unrestricted codes, by linear programming." (1972).
[15]
F. J. MacWilliams and N. J. A. Sloane. The theory of error correcting codes. Elsevier, 1977.
[16]
Addelman, S., & Kempthorne, O. (1961b). Orthogonal Main-Effect Plans. Technical Report ARL 79, Aeronautical Research Lab., Wright-Patterson Air Force Base, Ohio, Nov. 1961.
[17]
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
[18]
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
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Zoo Code ID: orthogonal_array

Cite as:
“Orthogonal array (OA)”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/orthogonal_array
BibTeX:
@incollection{eczoo_orthogonal_array, title={Orthogonal array (OA)}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/orthogonal_array} }
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“Orthogonal array (OA)”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/orthogonal_array

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/q-ary_digits/orthogonal_array.yml.