Applied and Computational Mathematics Seminar
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filed under:
Seminar
Rank and dimension of the kernel of Z_4-linear codes, by Cristina Fernández (Department of Information and Communications Engineering, Universitat Autònoma de Barcelona)
| What |
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|---|---|
| When |
Oct 13, 2008 from 04:10 pm to 05:00 pm |
| Where | Morton 227 |
| Contact Name | Vardges Melkonian |
| Contact Email | vardges@math.ohiou.edu |
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Abstract:
A code C is a quaternary linear code if C is a subgroup of Z_4^n. In this paper,
the rank and dimension of the kernel for Z_4-linear codes, which are the
corresponding binary codes of quaternary linear codes, are studied. The possible
values of these two parameters for Z_4-linear codes, giving lower and upper bounds,
are established. For each possible rank r between these bounds, the construction of
a Z_4-linear code with rank r is given. Equivalently, for each possible dimension of
the kernel k, the construction of a Z_4-linear code with dimension of the kernel k
is given. Finally, we consider the possible pairs of (r,k), and we construct
Z_4-linear codes for all possible pair (r,k) with rank r and dimension of the kernel
k.
