Abstract
In this paper, the rank and the dimension of the kernel for (binary) Hadamard codes of length a power of two are studied. In general, it is well-known that the rank of a Hadamard code of length n = 2t is a value in {t+1,..., n/2}. In the present paper, the range of possible values for the dimension of the kernel is computed and a construction of Hadamard codes of length n = 2t for each one of these values is given. Lower and upper bounds for the rank and dimension of the kernel of a Hadamard code of length n = 2t are also established. Finally, we construct Hadamard codes for all possible ranks and dimension of kernels between these bounds. © 2005 IEEE.
| Original language | English |
|---|---|
| Pages (from-to) | 3931-3937 |
| Journal | IEEE Transactions on Information Theory |
| Volume | 51 |
| DOIs | |
| Publication status | Published - 1 Nov 2005 |
Keywords
- Extended perfect codes
- Hadamard codes
- Hadamard matrices
- Kernel
- Rank