TY - JOUR

T1 - A Testing Set for Preparata-Like Codes

AU - Vasil’eva, A. Yu

N1 - This work was carried out within the framework of the state contract of the Sobolev Institute of Mathematics, project no. FWNF–2022–0017. Публикация для корректировки.

PY - 2023/6

Y1 - 2023/6

N2 - The reconstruction of an object of a given class by its intersection with some (so-calledtesting) set is studied. For the class, we consider Preparata-like codes, i.e., nonlinear codes oflength (Formula presented.), with code distance 5 and twice the size of a linear code of the same lengthand distance. Conditions are determined under which the union of a few concentric spheres formsa testing set for Preparata-like codes.

AB - The reconstruction of an object of a given class by its intersection with some (so-calledtesting) set is studied. For the class, we consider Preparata-like codes, i.e., nonlinear codes oflength (Formula presented.), with code distance 5 and twice the size of a linear code of the same lengthand distance. Conditions are determined under which the union of a few concentric spheres formsa testing set for Preparata-like codes.

KW - Hamming graph

KW - Krawtchouk polynomial

KW - Preparata-like code

KW - perfect code

KW - testing set

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85167515109&origin=inward&txGid=8fd84f4db4325b2fe7ce552e94937e76

UR - https://www.mendeley.com/catalogue/51ee353e-5054-3c0c-97ae-046ac7e8fbd4/

U2 - 10.1134/S1990478923020205

DO - 10.1134/S1990478923020205

M3 - Article

VL - 17

SP - 427

EP - 432

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 2

ER -