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JOURNALS // Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports] // Archive

Sib. Èlektron. Mat. Izv., 2024 Volume 21, Issue 2, Pages 897–913 (Mi semr1722)

Discrete mathematics and mathematical cybernetics

On the nonlinear codes, obtained from the Hamming code by switchings of $ijk$-components, as partially robust codes

D. I. Sikerina

State university of Aerospace Instrumentation, Bolshaya Morskaya St., 67, 190000, Saint-Petersburg, Russia

Abstract: In the paper, the partially robustness of nonlinear codes, obtained from the Hamming code by the known switching method of $ijk$-components, is proven. Such codes have less undetectable (miscorrected) errors than traditional linear error-correcting codes of the same length, which is a great advantage for modern technologies when multiple and repeating errors are common. An error detection and correction algorithm for this construction is presented.

Keywords: the Hamming code, $ijk$-component, partially robust code, error detection, error correction.

UDC: 621.391.15

MSC: 94B60

Received June 29, 2023, published November 1, 2024

Language: English

DOI: 10.33048/semi.2024.21.059



© Steklov Math. Inst. of RAS, 2025