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Classical and quantum evaluation codes at the trace roots
Año del Documento
IEEE Transactions on Information Theory, accepted for publication
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 with 4 elements which are records at http://codetables.de/.
Revisión por pares
This work was supported in part by the Spanish MINECO/FEDER (Grants No. MTM2015-65764-C3-2-P and MTM2015-69138-REDT), in part by the University Jaume I (Grant No. P1-1B2015-02), in part by The Danish Council for Independent Research (Grant No. DFF--4002-00367), and in part by RYC-2016-20208 (AEI/FSE/UE).
Version del Editor
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