تقرير
Hadamard Full Propelinear Codes of type Q. Rank and Kernel
| العنوان: | Hadamard Full Propelinear Codes of type Q. Rank and Kernel |
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| المؤلفون: | Rifà, J., Canedo, E. Suárez |
| سنة النشر: | 2017 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, 5B, 5E, 94B |
| الوصف: | Hadamard full propelinear codes (HFP-codes) are introduced and their equivalence with Hadamard groups is proven (on the other hand, it is already known the equivalence of Hadamard groups with relative $(4n,2,4n,2n)$-difference sets in a group and also with cocyclic Hadamard matrices). We compute the available values for the rank and dimension of the kernel of HFP-codes of type Q and we show that the dimension of the kernel is always 1 or $2$. We also show that when the dimension of the kernel is 2 then the dimension of the kernel of the transposed code is 1 (so, both codes are not equivalent). Finally, we give a construction method such that from an HFP-code of length $4n$, dimension of the kernel $k=2$, and maximum rank $r=2n$, we obtain an HFP-code of double length $8n$, dimension of the kernel $k=2$, and maximum rank $r=4n$. Comment: Submitted to Designs, Codes and Cryptography |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1709.02465 |
| رقم الأكسشن: | edsarx.1709.02465 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |