TY - CHAP
T1 - On rank and Kernel of ℤ4-linear codes
AU - Fernández-Córdoba, Cristina
AU - Pujol, Jaume
AU - Villanueva, Mercè
N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2008
Y1 - 2008
N2 - A code is a quaternary linear code if is a subgroup of ℤ4. In this paper, the rank and dimension of the kernel for ℤ4- linear codes, which are the corresponding binary codes of quaternary linear codes, are studied. The possible values of these two parameters for ℤ4-linear codes, giving lower and upper bounds, are established. For each possible rank r between these bounds, the construction of a ℤ4-linear code with rank r is given. Equivalently, for each possible dimension of the kernel k, the construction of a ℤ4- linear code with dimension of the kernel k is given.
AB - A code is a quaternary linear code if is a subgroup of ℤ4. In this paper, the rank and dimension of the kernel for ℤ4- linear codes, which are the corresponding binary codes of quaternary linear codes, are studied. The possible values of these two parameters for ℤ4-linear codes, giving lower and upper bounds, are established. For each possible rank r between these bounds, the construction of a ℤ4-linear code with rank r is given. Equivalently, for each possible dimension of the kernel k, the construction of a ℤ4- linear code with dimension of the kernel k is given.
KW - ℤ-linear codes
KW - Kernel
KW - Quaternary codes
KW - Rank
UR - https://www.scopus.com/pages/publications/52149122972
U2 - 10.1007/978-3-540-87448-5_6
DO - 10.1007/978-3-540-87448-5_6
M3 - Chapter
AN - SCOPUS:52149122972
SN - 354087447X
SN - 9783540874478
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 46
EP - 55
BT - Coding Theory and Applications - Second International Castle Meeting, ICMCTA 2008, Proceedings
ER -