DocumentCode
47980
Title
Construction of Hadamard 
-Codes for Each Allowable Value of the Rank and Dimension of the Kernel
Author
Montolio, Pere ; Rifa, Josep
Author_Institution
Dept. of Inf. & Commun. Eng., Univ. Autonoma de Barcelona, Bellaterra, Spain
Volume
61
Issue
4
fYear
2015
fDate
Apr-15
Firstpage
1948
Lastpage
1958
Abstract
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.
Keywords
Hadamard codes; algebraic codes; binary codes; group codes; group theory; Gray map; Hadamard code construction; Z2Z4Q8 codes; binary codes; dimension allowable value; linear code semidirect product; quaternionic group; rank allowable value; Error correction; Error correction codes; Generators; Kernel; Niobium; Shape; Vectors; $mathbb {Z}_{2} mathbb {Z}_{4} {Q}_{8}$ -codes; $mathbb {Z}_{2} mathbb {Z}_{4}$ -codes; Dimension of the kernel; Hadamard codes; Z2Z4-codes; Z2Z4Q8-codes; error-correcting codes; rank;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/TIT.2015.2398869
Filename
7029629
Link To Document