Listar Departament: Matemàtiques por autoría "8f6be33c-c170-4ab0-8df8-0e347ea567e3"
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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 ... -
Decoding of matrix-product codes
World Scientific Publishing Company (2013-06)We propose a decoding algorithm for the (u | u + v)-construction that decodes up to half of the minimum distance of the linear code. We extend this algorithm for a class of matrix-product codes in two different ways. In ... -
Entanglement-assisted quantum error-correcting codes from RS codes and BCH codes with extension degree 2
Springer Nature (2021-05-03)Entanglement-assisted quantum error-correcting codes (EAQECCs) constructed from Reed–Solomon codes and BCH codes are considered in this work. It is provided a complete and explicit formula for the parameters of EAQECCs ...
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Entanglement-assisted quantum error-correcting codes over arbitrary finite fields
Springer Verlag (2019)We prove that the known formulae for computing the optimal number of maximally entangled pairs required for entanglement-assisted quantum error-correcting codes (EAQECCs) over the binary field hold for codes over arbitrary ...
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Improved constructions of nested code pairs
IEEE (2017-09)Two new constructions of linear code pairs C2 ⊂ C1 are given for which the codimension and the relative minimum distances M1(C1,C2), M1(C┴2 , C┴1) are good. By this we mean that for any two out of the three parameters the ...
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List Decoding of Matrix-Product Codes from nested codes: an application to Quasi-Cyclic codes
American Institute of Mathematical Sciences (2012-01-30)A list decoding algorithm for matrix-product codes is provided when C1, . . . , Cs are nested linear codes and A is a non-singular by columns matrix. We estimate the probability of getting more than one codeword as output ...
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List decoding of repeated codes
Springer (2013-08)Assuming that we have a soft-decision list decoding algorithm of a linear code, a new hard-decision list decoding algorithm of its repeated code is proposed in this article. Although repeated codes are not used for ...
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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 ...
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New quantum codes from evaluation and matrix-product codes
Elsevier (2014-07)Stabilizer codes obtained via CSS code construction and Steane's enlargement of subfield-subcodes and matrix-product codes coming from generalized Reed-Muller, hyperbolic and affine variety codes are studied. Stabilizer ...
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On the classification of exceptional planar functions over Fp
Springer Netherlands (2014-12)We will present many strong partial results towards a classification of exceptional planar/PN monomial functions on finite fields. The techniques we use are the Weil bound, Bézout’s theorem, and Bertini’s theorem.
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On the distance of stabilizer quantum codes from J-affine variety codes
Springer Verlag (2017)Self-orthogonal J-affine variety codes have been successfully used to obtain quantum stabilizer codes with excellent parameters. In a previous paper we gave formulae for the dimension of this family of quantum codes, but ...
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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 ...
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Optimal (r,δ)-LRCs from monomial-Cartesian codes and their subfield-subcodes
Springer (2024-05-02)We study monomial-Cartesian codes (MCCs) which can be regarded as (r,δ)-locally recoverable codes (LRCs). These codes come with a natural bound for their minimum distance and we determine those giving rise to (r,δ)-optimal ...
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Proof of a conjecture of Segre and Bartocci on monomial hyperovals in projective planes
Springer US (2012-02)The existence of certain monomial hyperovals D(xk) in the finite Desarguesian projective plane PG(2, q), q even, is related to the existence of points on certain projective plane curves gk(x, y, z). Segre showed that some ...
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Quantum codes from a new construction of self-orthogonal algebraic geometry codes
Springer (2020)We present new quantum codes with good parameters which are constructed from self-orthogonal algebraic geometry codes. Our method permits a wide class of curves to be used in the formation of these codes. These results ...
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Quantum codes from affine variety codes and their subfield-subcodes
Springer (2015-07)We use affine variety codes and their subfield-subcodes to obtain quantum stabilizer codes via the CSS code construction. With this procedure we get codes with good parameters, some of them exceeding the CSS quantum ...
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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 ...
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Stabilizer quantum codes from J -affine variety codes and a new Steane-like enlargement
Springer (2014-09)New stabilizer codes with parameters better than the ones available in the literature are provided in this work, in particular quantum codes with parameters [[127,63,≥12]]2 and [[63,45,≥6]]4 that are records. These codes ...
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Steane enlargement of entanglement-assisted quantum error-correcting codes
Springer (2023-08-07)We introduce a Steane-like enlargement procedure for entanglement-assisted quantum error-correcting codes (EAQECCs) obtained by considering Euclidean inner product. We give formulae for the parameters of these enlarged ...
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The dimension of subcode-subfields of shortened generalized Reed–Solomon codes
Springer US (2012-03)Reed–Solomon (RS) codes are among the most ubiquitous codes due to their good parameters as well as efficient encoding and decoding procedures. However, RS codes suffer from having a fixed length. In many applications where ...
