On the structure of non-full-rank perfect q-ary codes Full article
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Advances in Mathematics of Communications
ISSN: 1930-5346 , E-ISSN: 1930-5338 |
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| Output data | Year: 2011, Volume: 5, Number: 2, Pages: 149-156 Pages count : 8 DOI: 10.3934/amc.2011.5.149 | ||||||
| Tags | lower bound, q-ary codes, perfect codes, components | ||||||
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Abstract:
The Krotov combining construction of perfect 1-error-correcting binary codes from 2000 and a theorem of Heden saying that every non-full-rank perfect 1-error-correcting binary code can be constructed by this combining construction is generalized to the q-ary case. Simply speaking, every non-full-rank perfect code C is the union of a well-defined family of (mu) over bar -components K_\mu, where \mu over bar belongs to an "outer" perfect code C', and these components are at distance three from each other. Components from distinct codes can thus freely be combined to obtain new perfect codes. The Phelps general product construction of perfect binary code from 1984 is generalized to obtain \mu-components, and new lower bounds on the number of perfect 1-error-correcting q-ary codes are presented.
Cite:
Heden O.
, Krotov D.S.
On the structure of non-full-rank perfect q-ary codes
Advances in Mathematics of Communications. 2011. V.5. N2. P.149-156. DOI: 10.3934/amc.2011.5.149 WOS Scopus РИНЦ OpenAlex
On the structure of non-full-rank perfect q-ary codes
Advances in Mathematics of Communications. 2011. V.5. N2. P.149-156. DOI: 10.3934/amc.2011.5.149 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Mar 31, 2010 |
| Accepted: | Aug 31, 2010 |
Identifiers:
| Web of science: | WOS:000293562800002 |
| Scopus: | 2-s2.0-79955752862 |
| Elibrary: | 16991923 |
| OpenAlex: | W1525308658 |