Classical and Quantum Evaluation Codes at the Trace Roots

@article{Galindo2019ClassicalAQ,
  title={Classical and Quantum Evaluation Codes at the Trace Roots},
  author={C. Galindo and F. Hernando and D. Ruano},
  journal={IEEE Transactions on Information Theory},
  year={2019},
  volume={65},
  pages={2593-2602}
}
  • C. Galindo, F. Hernando, D. Ruano
  • Published 2019
  • Computer Science, Mathematics
  • IEEE Transactions on Information Theory
  • 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 <uri>http://codetables.de/</uri>. Moreover, we obtain several… CONTINUE READING

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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 62 REFERENCES
    On the distance of stabilizer quantum codes from J-affine variety codes
    12
    New quantum codes from evaluation and matrix-product codes
    23
    Nonbinary Stabilizer Codes Over Finite Fields
    330
    Quantum twisted codes
    114
    Stabilizer quantum codes from J-affine variety codes and a new Steane-like enlargement
    22
    On Quantum and Classical BCH Codes
    211
    Quantum Error Correction Via Codes Over GF(4)
    716
    Evaluation codes from order domain theory
    45
    Quantum error detection II: Bounds
    47
    On optimal quantum codes
    154