1,586 research outputs found
On optimal quantum codes
We present families of quantum error-correcting codes which are optimal in
the sense that the minimum distance is maximal. These maximum distance
separable (MDS) codes are defined over q-dimensional quantum systems, where q
is an arbitrary prime power. It is shown that codes with parameters
[[n,n-2d+2,d]]_q exist for all 3 <= n <= q and 1 <= d <= n/2+1. We also present
quantum MDS codes with parameters [[q^2,q^2-2d+2,d]]_q for 1 <= d <= q which
additionally give rise to shortened codes [[q^2-s,q^2-2d+2-s,d]]_q for some s.Comment: Accepted for publication in the International Journal of Quantum
Informatio
On the Weight Distribution of Codes over Finite Rings
Let R > S be finite Frobenius rings for which there exists a trace map T from
R onto S as left S modules. Let C:= {x -> T(ax + bf(x)) : a,b in R}. Then C is
an S-linear subring-subcode of a left linear code over R. We consider functions
f for which the homogeneous weight distribution of C can be computed. In
particular, we give constructions of codes over integer modular rings and
commutative local Frobenius that have small spectra.Comment: 18 p
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