Abstract
© 2015 IEEE. This paper deals with Hadamard ℤ2ℤ4Q8 -codes, which are binary codes after a Gray map from a subgroup of direct products of ℤ2, ℤ4, and Q8, where Q8 is the quaternionic group. In a previous work, these codes were classified in five shapes. In this paper, we analyze the allowable range of values for the rank and dimension of the kernel, which depends on the particular shape of the code. We show that all these codes can be represented in a standard form, from a set of generators, which can help in understanding the characteristics of each shape. The main results we present are the characterization of Hadamard ℤ2ℤ4Q8-codes as a quotient of a semidirect product of ℤ2ℤ4-linear codes and the construction of Hadamard ℤ2ℤ4Q8-codes with each allowable pair of values for the rank and dimension of the kernel.
| Original language | English |
|---|---|
| Article number | 7029629 |
| Pages (from-to) | 1948-1958 |
| Journal | IEEE Transactions on Information Theory |
| Volume | 61 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 1 Apr 2015 |
Keywords
- Dimension of the kernel
- Hadamard codes
- error-correcting codes
- rank
- ℤ ℤ -codes 2 4
- ℤ ℤ Q -codes 2 4 8