Embedding in q-ary 1-perfect codes and partitions Full article
| Journal |
Discrete Mathematics
ISSN: 0012-365X , E-ISSN: 1872-681X |
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| Output data | Year: 2015, Volume: 338, Number: 11, Pages: 1856-1859 Pages count : 4 DOI: 10.1016/j.disc.2015.04.014 | ||||
| Tags | Embedding, q-ary code, 1-code, 1-perfect code, Partitions, Hamming code | ||||
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Abstract:
It is proved that every 1-error-correcting code over a finite field can be embedded in a 1-perfect code of some larger length. Embedding in this context means that the original code is a subcode of the resulting 1-perfect code and can be obtained from it by repeated shortening. Further, the result is generalized to partitions: every partition of the Hamming space into 1-error-correcting codes can be embedded in a partition of a space of some larger dimension into 1-perfect codes. For the partitions, the embedding length is close to the theoretical bound for the general case and optimal for the binary case.
Cite:
Krotov D.S.
, Sotnikova E.V.
Embedding in q-ary 1-perfect codes and partitions
Discrete Mathematics. 2015. V.338. N11. P.1856-1859. DOI: 10.1016/j.disc.2015.04.014 WOS Scopus РИНЦ OpenAlex
Embedding in q-ary 1-perfect codes and partitions
Discrete Mathematics. 2015. V.338. N11. P.1856-1859. DOI: 10.1016/j.disc.2015.04.014 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Dec 15, 2014 |
| Accepted: | Apr 13, 2015 |
| Published online: | Jun 5, 2015 |
Identifiers:
| Web of science: | WOS:000358459300003 |
| Scopus: | 2-s2.0-84930686196 |
| Elibrary: | 24046230 |
| OpenAlex: | W1875081033 |