Results 11 to 20 of about 74,437 (278)
Combinatorial batch codes [PDF]
Advances in Mathematics of Communications, 2008 In this paper, we study batch codes, which were introduced by Ishai, Kushilevitz, Ostrovsky and Sahai in [4]. A batch code specifies a method to distribute a database of [n] items among [m] devices (servers) in such a way that any [k] items can be ...
Paterson, Maura B. +2 more
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Multiset Combinatorial Batch Codes [PDF]
2017 IEEE International Symposium on Information Theory (ISIT), 2017 Batch codes, first introduced by Ishai, Kushilevitz, Ostrovsky, and Sahai, mimic a distributed storage of a set of $n$ data items on $m$ servers, in such a way that any batch of $k$ data items can be retrieved by reading at most some $t$ symbols from ...
Silberstein, Natalia +2 more
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Combinatorial polarization, code loops, and codes of high level [PDF]
International Journal of Mathematics and Mathematical Sciences, 2004 We first find the combinatorial degree of any map f:V→F, where F is a finite field and V is a finite-dimensional vector space over F. We then simplify and generalize a certain construction, due to Chein and Goodaire, that was used in characterizing code
Petr Vojtechovský
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Derandomized Construction of Combinatorial Batch Codes [PDF]
, 2015 Combinatorial Batch Codes (CBCs), replication-based variant of Batch Codes introduced by Ishai et al. in STOC 2004, abstracts the following data distribution problem: $n$ data items are to be replicated among $m$ servers in such a way that any $k$ of the
B Bollobás +13 more
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Bio-Constrained Codes with Neural Network for Density-Based DNA Data Storage
Mathematics, 2022 DNA has evolved as a cutting-edge medium for digital information storage due to its extremely high density and durable preservation to accommodate the data explosion. However, the strings of DNA are prone to errors during the hybridization process.
Abdur Rasool +3 more
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A Combinatorial Approach to Flag Codes
CoRR, 2021 In network coding, a flag code is a collection of flags, that is, sequences of nested subspaces of a vector space over a finite field. Due to its definition as the sum of the corresponding subspace distances, the flag distance parameter encloses a hidden combinatorial structure.
Clementa Alonso-González +1 more
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On the generalized Hamming weights of certain Reed–Muller-type codes
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020 There is a nice combinatorial formula of P. Beelen and M. Datta for the r-th generalized Hamming weight of an a ne cartesian code. Using this combinatorial formula we give an easy to evaluate formula to compute the r-th generalized Hamming weight for a ...
González-Sarabia Manuel +2 more
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Кібернетика та комп'ютерні технології, 2022 Introduction. The application of binary-reflected (mirror, reflexive) Gray codes for solving combinatorial problems with pseudo-Boolean functions (polynomials from Boolean variables) is considered.
Oleksandr Trofymchuk +4 more
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Three Combinatorial Perspectives on Minimal Codes [PDF]
SIAM Journal on Discrete Mathematics, 2022 27 ...
Gianira N. Alfarano +3 more
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General Fractional Repetition Codes From Combinatorial Designs
IEEE Access, 2017 Fractional repetition codes are a class of distributed storage codes dedicated to optimize the node repair performance, i.e., they enable uncoded exact repairs with minimum bandwidth consumption.
Bing Zhu, Hui Li, Shuo-Yen Robert Li
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