Results 11 to 20 of about 190,937 (260)
Squares of matrix-product codes [PDF]
Finite Fields and Their Applications, 2020 The component-wise or Schur product $C*C'$ of two linear error correcting codes $C$ and $C'$ over certain finite field is the linear code spanned by all component-wise products of a codeword in $C$ with a codeword in $C'$. When $C=C'$, we call the product the square of $C$ and denote it $C^{*2}$.
Ignacio Cascudo +2 more
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Product construction of affine codes [PDF]
2014 IEEE International Symposium on Information Theory, 2014 Binary matrix codes with restricted row and column weights are a desirable method of coded modulation for power line communication. In this work, we construct such matrix codes that are obtained as products of affine codes - cosets of binary linear codes. Additionally, the constructions have the property that they are systematic.
Yeow Meng Chee +3 more
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Fault-tolerant gates via homological product codes [PDF]
Quantum, 2019 A method for the implementation of a universal set of fault-tolerant logical gates is presented using homological product codes. In particular, it is shown that one can fault-tolerantly map between different encoded representations of a given logical ...
Tomas Jochym-O'Connor
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Mathematics, 2023 Let k,m be positive integers and F2m be a finite field of order 2m of characteristic 2. The primary goal of this paper is to study the structural properties of cyclic codes over the ring Sk=F2m[v1,v2,…,vk]⟨vi2−αivi,vivj−vjvi⟩, for i,j=1,2,3,…,k, where αi
Shakir Ali +3 more
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DECODING OF MATRIX-PRODUCT CODES [PDF]
Journal of Algebra and Its Applications, 2013 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 some cases, one can decode beyond the error-correction capability of the code.
Hernando, Fernando, Ruano Benito, Diego
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On quantum tensor product codes [PDF]
Quantum Information and Computation, 2017 We present a general framework for the construction of quantum tensor product codes (QTPC). In a classical tensor product code (TPC), its parity check matrix is constructed via the tensor product of parity check matrices of the two component codes. We show that by adding some constraints on the component codes, several classes of dual-containing TPCs ...
Jihao Fan +3 more
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Fault-Tolerant Gates on Hypergraph Product Codes
Physical Review X, 2021 Quantum computers have the capacity to change the landscape of computing. To make these devices robust to experimental imperfections, we require some form of quantum error correction. Current approaches focus on topological codes, as they appear to be in
Anirudh Krishna, David Poulin
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On tensor products of CSS codes [PDF]
Annales de l’Institut Henri Poincaré D, Combinatorics, Physics and their Interactions, 2019 CSS codes are in one-to-one correspondance with length 3 chain complexes. The latter are naturally endowed with a tensor product \otimes which induces a similar operation on the former. We investigate this operation, and in particular its behavior with regard to minimum distances. Given
Audoux, Benjamin, Couvreur, Alain
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Bias-tailored quantum LDPC codes [PDF]
Quantum, 2023 Bias-tailoring allows quantum error correction codes to exploit qubit noise asymmetry. Recently, it was shown that a modified form of the surface code, the XZZX code, exhibits considerably improved performance under biased noise.
Joschka Roffe +4 more
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Product perfect codes and steganography [PDF]
Digital Signal Processing, 2009 A new coding technique to be used in steganography is evaluated. The performance of this new technique is computed and comparisons with the well-known theoretical upper bound, Hamming upper bound and basic LSB are established.
Helena Rifà-Pous, Josep Rifà
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