Geodesic
On codes with unique decoding to the nearest
Prikladnaya Diskretnaya Matematika. Supplement, no. 17 (2024), pp. 138-140

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The paper is devoted to the problem No. 7 of the NSUCRYPTO 2023 Olympiad on the description of an interesting class of codes: with unique decoding to the nearest codeword in the Hamming metric. The possibility of representing the code $C$ as a matroid is proved and an intermediate solution is given in the case when a set of bits $B$ such that there is a two-bit word containing it that is decoded not at $z = 0$ coincides with all positions of the code bits.
Mots-clés : NSUCRYPTO, code
Keywords: Hamming weight, matroid. 
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     author = {D. S. Ananichev and K. L. Geut and S. S. Titov},
     title = {On codes with unique decoding to the nearest},
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     publisher = {mathdoc},
     number = {17},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2024_17_a34/}
}
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D. S. Ananichev; K. L. Geut; S. S. Titov. On codes with unique decoding to the nearest. Prikladnaya Diskretnaya Matematika. Supplement, no. 17 (2024), pp. 138-140. http://geodesic.mathdoc.fr/item/PDMA_2024_17_a34/