2,904 research outputs found
From Skew-Cyclic Codes to Asymmetric Quantum Codes
We introduce an additive but not -linear map from
to and exhibit some of its interesting
structural properties. If is a linear -code, then is an
additive -code. If is an additive cyclic code then
is an additive quasi-cyclic code of index . Moreover, if is a module
-cyclic code, a recently introduced type of code which will be
explained below, then is equivalent to an additive cyclic code if is
odd and to an additive quasi-cyclic code of index if is even. Given any
-code , the code is self-orthogonal under the trace
Hermitian inner product. Since the mapping preserves nestedness, it can be
used as a tool in constructing additive asymmetric quantum codes.Comment: 16 pages, 3 tables, submitted to Advances in Mathematics of
Communication
Skew Cyclic codes over \F_q+u\F_q+v\F_q+uv\F_q
In this paper, we study skew cyclic codes over the ring
R=\F_q+u\F_q+v\F_q+uv\F_q, where , and
is an odd prime. We investigate the structural properties of skew cyclic codes
over through a decomposition theorem. Furthermore, we give a formula for
the number of skew cyclic codes of length over $R.
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