TY - JOUR
T1 - Construction of hadamard ℤ2ℤ4Q8-codes for each allowable value of the rank and dimension of the kernel
AU - Montolio, Pere
AU - Rifà, Josep
PY - 2015/4/1
Y1 - 2015/4/1
N2 - © 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.
AB - © 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.
KW - Dimension of the kernel
KW - Hadamard codes
KW - error-correcting codes
KW - rank
KW - ℤ ℤ -codes 2 4
KW - ℤ ℤ Q -codes 2 4 8
U2 - 10.1109/TIT.2015.2398869
DO - 10.1109/TIT.2015.2398869
M3 - Article
SN - 0018-9448
VL - 61
SP - 1948
EP - 1958
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 4
M1 - 7029629
ER -