Combinatorial polarization, code loops, and codes of high level
We first find the combinatorial degree of any map f:V→F, where F is a finite field and V is a finite-dimensional vector space over F. We then simplify and generalize a certain construction, due to Chein and Goodaire, that was used in characterizing code loops as finite Moufang loops that possess at...
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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204306241 |
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| _version_ | 1832564217647988736 |
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| author | Petr Vojtechovský |
| author_facet | Petr Vojtechovský |
| author_sort | Petr Vojtechovský |
| collection | DOAJ |
| description | We first find the combinatorial degree of any map f:V→F, where F is a finite field and V
is a finite-dimensional
vector space over F. We then simplify and generalize a certain
construction, due to Chein and Goodaire, that was used in
characterizing code loops as finite Moufang loops that possess at
most two squares. The construction yields binary codes of high
divisibility level with prescribed Hamming weights of
intersections of codewords. |
| format | Article |
| id | doaj-art-b3f3eb1a83844de486468658a19968b3 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-b3f3eb1a83844de486468658a19968b32025-02-03T01:11:35ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004291533154110.1155/S0161171204306241Combinatorial polarization, code loops, and codes of high levelPetr Vojtechovský0Department of Mathematics, University of Denver, 2360 S. Gaylord Street, Denver, CO 80208, USAWe first find the combinatorial degree of any map f:V→F, where F is a finite field and V is a finite-dimensional vector space over F. We then simplify and generalize a certain construction, due to Chein and Goodaire, that was used in characterizing code loops as finite Moufang loops that possess at most two squares. The construction yields binary codes of high divisibility level with prescribed Hamming weights of intersections of codewords.http://dx.doi.org/10.1155/S0161171204306241 |
| spellingShingle | Petr Vojtechovský Combinatorial polarization, code loops, and codes of high level International Journal of Mathematics and Mathematical Sciences |
| title | Combinatorial polarization, code loops, and codes of high level |
| title_full | Combinatorial polarization, code loops, and codes of high level |
| title_fullStr | Combinatorial polarization, code loops, and codes of high level |
| title_full_unstemmed | Combinatorial polarization, code loops, and codes of high level |
| title_short | Combinatorial polarization, code loops, and codes of high level |
| title_sort | combinatorial polarization code loops and codes of high level |
| url | http://dx.doi.org/10.1155/S0161171204306241 |
| work_keys_str_mv | AT petrvojtechovsky combinatorialpolarizationcodeloopsandcodesofhighlevel |