Geodesic
A testing set for Preparata-like codes
Diskretnyj analiz i issledovanie operacij, Tome 30 (2023) no. 2, pp. 5-14

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The reconstruction of an object of a given class by its intersection with some (so-called testing) set is studied. For the class, we consider Preparata-like codes, i. e. nonlinear codes of length $n=2^{2m}-1,$ $m=2,3,\dots,$ with code distance $5$ and twice the size of a linear code of the same length and distance. We determine conditions under which the union of a few concentric spheres forms the testing set for Preparata-like codes.
Keywords: Hamming graph, Preparata code, perfect code, testing set
Mots-clés : Krawtchouk polynomial. 
@article{DA_2023_30_2_a0,
     author = {A. Yu. Vasil'eva},
     title = {A testing set for {Preparata-like} codes},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {5--14},
     publisher = {mathdoc},
     volume = {30},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2023_30_2_a0/}
}
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A. Yu. Vasil'eva. A testing set for Preparata-like codes. Diskretnyj analiz i issledovanie operacij, Tome 30 (2023) no. 2, pp. 5-14. http://geodesic.mathdoc.fr/item/DA_2023_30_2_a0/