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A Testing Set for Preparata-Like Codes

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Abstract

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. Conditions are determined under which the union of a few concentric spheres forms a testing set for Preparata-like codes.

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Funding

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

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia

    A. Yu. Vasil’eva

  2. Novosibirsk State University, Novosibirsk, 630090, Russia

    A. Yu. Vasil’eva

Authors
  1. A. Yu. Vasil’eva
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Correspondence to A. Yu. Vasil’eva.

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Translated by V. Potapchouck

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Vasil’eva, A.Y. A Testing Set for Preparata-Like Codes. J. Appl. Ind. Math. 17, 427–432 (2023). https://doi.org/10.1134/S1990478923020205

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  • DOI: https://doi.org/10.1134/S1990478923020205

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