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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |