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Classical and Quantum Evaluation Codes at the Trace Roots | IEEE Journals & Magazine | IEEE Xplore

Classical and Quantum Evaluation Codes at the Trace Roots


Abstract:

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 thes...Show More

Abstract:

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 F4 which are records at http://codetables.de/.
Published in: IEEE Transactions on Information Theory ( Volume: 65, Issue: 4, April 2019)
Page(s): 2593 - 2602
Date of Publication: 02 September 2018

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