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Classical and Quantum Evaluation Codesat the Trace Roots
(IEEE, 2019-04)
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 ...
Asymmetric Entanglement-Assisted Quantum Error-Correcting Codes and BCH Codes
(IEEE, 2020-01-17)
The concept of asymmetric entanglement-assisted quantum error-correcting code (asymmetric EAQECC) is introduced in this article. Codes of this type take advantage of the asymmetry in quantum errors since phase-shift errors ...
Quasi-cyclic constructions of quantum codes
(Elsevier, 2018-07)
We give sufficient conditions for self-orthogonality with respect to symplec-
tic, Euclidean and Hermitian inner products of a wide family of quasi-cyclic codes of index
two. We provide lower bounds for the symplectic ...
Foliations with isolated singularities on Hirzebruch surfaces
(De Gruyter, 2021)
We study foliations ℱ on Hirzebruch surfaces Sδ and prove that, similarly to those on the projective plane, any ℱ can be represented by a bi-homogeneous polynomial affine 1-form. In case ℱ has isolated singularities, we ...
On the generalization of the construction of quantum codes from Hermitian self-orthogonal codes
(Springer, 2022-03-21)
Many q-ary stabilizer quantum codes can be constructed from Hermitian self-orthogonal q2-ary linear codes. This result can be generalized to q2m-ary linear codes, m>1. We give a result for easily obtaining quantum codes ...
Using videos to improve oral presentation skills in distance learning engineering master's degrees
(Taylor & Francis, 2019-09-11)
In this paper we present a pilot study to improve the learning process on distance learning Engineering master's degrees. We propose an activity where the students individually produce a video in which they explain the ...
New binary and ternary LCD codes
(IEEE, 2018-05-09)
LCD codes are linear codes with important cryptographic applications. Recently, a method has been presented
to transform any linear code into an LCD code with the same parameters when it is supported on a finite field ...
Locally recoverable J-affine variety codes
(2020-06)
A locally recoverable (LRC) code is a code over a finite eld Fq such that
any erased coordinate of a codeword can be recovered from a small number of other
coordinates in that codeword. We construct LRC codes correcting ...
Stabilizer quantum codes defined by trace-depending polynomials
(Elsevier, 2022-12-29)
Quantum error-correcting codes with good parameters can be constructed by evaluating polynomials at the roots of the polynomial trace [18]. In this paper, we propose to evaluate polynomials at the roots of trace-depending ...
Seshadri-type constants and Newton-Okounkov bodies for non-positive at infinity valuations of Hirzebruch surfaces
(Taylor and Francis, 2023-02-01)
We consider flags E• = {X ⊃ E ⊃ {q}}, where E is an exceptional
divisor defining a non-positive at infinity divisorial valuation νE of a Hirzebruch
surface Fδ , q a point in E and X the surface given by νE , and determine ...