167 research outputs found
Asymmetric Quantum Codes: New Codes from Old
In this paper we extend to asymmetric quantum error-correcting codes (AQECC)
the construction methods, namely: puncturing, extending, expanding, direct sum
and the (u|u + v) construction. By applying these methods, several families of
asymmetric quantum codes can be constructed. Consequently, as an example of
application of quantum code expansion developed here, new families of
asymmetric quantum codes derived from generalized Reed-Muller (GRM) codes,
quadratic residue (QR), Bose-Chaudhuri-Hocquenghem (BCH), character codes and
affine-invariant codes are constructed.Comment: Accepted for publication Quantum Information Processin
Classical and Quantum Evaluation Codesat the Trace Roots
We introduce a new class of evaluation linear codes by evaluating polynomials at the roots of a suitable trace function. We give conditions for self-orthogonality of these codes and their subfield-subcodes with respect to the Hermitian inner product. They allow us to construct stabilizer quantum codes over several finite fields which substantially improve the codes in the literature. For the binary case, we obtain records at http://codetables.de/. Moreover, we obtain several classical linear codes over the field F 4 which are records at http://codetables.de/
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