Real name:
First Name:
Denis
Last Name:
Krotov
Affiliation:
Sobolev Institute of Mathematics
Datasets & Competitions
This dataset is devoted to 1-perfect codes. Currently, it is mainly focused on the concatenated ternary perfect codes, but there is also an additional content, see (3+) below, (1-2) This dataset contains all inequivalent concatenated ternary 1-perfect codes of length 13. Additionally, it contains some components necessary to obtain such concatenated codes, namely, collections of disjoint ternary distance-3 Reed-Muller-like codes of length 9, see p.(1) below.
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A Latin square of order q is a q×q array with elements from {0,1,...,q-1} such that each value occurs exactly once in each row and column. Two Latin squares G and L are orthogonal if (G(x,y), L(x,y)) = (u,v) has exactly one solution for each (u,v) from {0,1,...,q-1}×{0,1,...,q-1}.
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The dataset is the result of exhaustive search of primary extended 1-perfect unitrades in the 10-cube, or, equivalently, triangle-free 5-regular connected induced subgraphs of the halved 10-cube. We list representatives of all the 38 equivalence classes.
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