Listar por autoría "b55bc5f7-1b6a-440d-b4f6-a6f44a37856f"
Mostrando ítems 1-13 de 13
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Asymmetric Entanglement-Assisted Quantum Error-Correcting Codes and BCH Codes
Galindo, Carlos; Hernando, Fernando; Matsumoto, Ryutaroh; Ruano, Diego 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 ... -
Classical and Quantum Evaluation Codesat the Trace Roots
Galindo, Carlos; Hernando, Fernando; Ruano, Diego 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 ... -
Decoding of matrix-product codes
Hernando, Fernando; Ruano, Diego 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
Galindo, Carlos; Hernando, Fernando; Ruano, Diego 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 ... -
Entanglement-assisted quantum error-correcting codes over arbitrary finite fields
Galindo, Carlos; Hernando, Fernando; Matsumoto, Ryutaroh; Ruano, Diego 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 ... -
Improved constructions of nested code pairs
Galindo, Carlos; Geil, Olav; Hernando, Fernando; Ruano, Diego 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 ... -
List Decoding of Matrix-Product Codes from nested codes: an application to Quasi-Cyclic codes
Hernando, Fernando; Hoholdt, Tom; Ruano, Diego 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 ... -
List decoding of repeated codes
Hernando, Fernando; O'Sullivan, Michael E.; Ruano, Diego 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 ... -
New binary and ternary LCD codes
Galindo, Carlos; Geil, Olav; Hernando, Fernando; Ruano, Diego 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 ... -
New quantum codes from evaluation and matrix-product codes
Galindo, Carlos; Hernando, Fernando; Ruano, Diego 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 ... -
On the distance of stabilizer quantum codes from J-affine variety codes
Galindo, Carlos; Geil, Olav; Hernando, Fernando; Ruano, Diego 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 ... -
Stabilizer quantum codes defined by trace-depending polynomials
Galindo, Carlos; Hernando, Fernando; Martín-Cruz, Helena; Ruano, Diego 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 ... -
Stabilizer quantum codes from J -affine variety codes and a new Steane-like enlargement
Galindo, Carlos; Hernando, Fernando; Ruano, Diego 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 ...