Abstract
A code \({\cal C}\) is a quaternary linear code if \({\cal C}\) is a subgroup of ℤ . 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.
This work was supported in part by the Spanish MEC and the European FEDER under Grants MTM2006-03250 and TSI2006-14005-C02-01.
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Fernández-Córdoba, C., Pujol, J., Villanueva, M. (2008). On Rank and Kernel of ℤ4-Linear Codes. In: Barbero, Á. (eds) Coding Theory and Applications. Lecture Notes in Computer Science, vol 5228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87448-5_6
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DOI: https://doi.org/10.1007/978-3-540-87448-5_6
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