Zobrazeno 1 - 10
of 440
pro vyhledávání: '"Etzion, Tuvi"'
Motivated by a repair problem for fractional repetition codes in distributed storage, each block of any Steiner quadruple system (SQS) of order $v$ is partitioned into two pairs. Each pair in such a partition is called a nested design pair and its mu
Externí odkaz:
http://arxiv.org/abs/2410.14417
Autor:
Etzion, Tuvi
A de Bruijn arrays code is a set of $r \times s$ binary doubly-periodic arrays such that each binary $n \times m$ matrix is contained exactly once as a window in one of the arrays. Such a set of arrays can be viewed as a two-dimensional generalizatio
Externí odkaz:
http://arxiv.org/abs/2407.18122
Enzymatic DNA labeling is a powerful tool with applications in biochemistry, molecular biology, biotechnology, medical science, and genomic research. This paper contributes to the evolving field of DNA-based data storage by presenting a formal framew
Externí odkaz:
http://arxiv.org/abs/2405.08475
Autor:
Dinh, Thi Xinh, Le, Ba Thong, Dau, Son Hoang, Boztas, Serdar, Kruglik, Stanislav, Kiah, Han Mao, Viterbo, Emanuele, Etzion, Tuvi, Chee, Yeow Meng
We generalize the problem of recovering a lost/erased symbol in a Reed-Solomon code to the scenario in which some side information about the lost symbol is known. The side information is represented as a set $S$ of linearly independent combinations o
Externí odkaz:
http://arxiv.org/abs/2405.07180
To measure repair latency at helper nodes, we introduce a new metric called skip cost that quantifies the number of contiguous sections accessed on a disk. We provide explicit constructions of zigzag codes and fractional repetition codes that incur z
Externí odkaz:
http://arxiv.org/abs/2405.03614
Nearly perfect packing codes are those codes that meet the Johnson upper bound on the size of error-correcting codes. This bound is an improvement to the sphere-packing bound. A related bound for covering codes is known as the van Wee bound. Codes th
Externí odkaz:
http://arxiv.org/abs/2405.00258
An $(m,n,R)$-de Bruijn covering array (dBCA) is a doubly periodic $M \times N$ array over an alphabet of size $q$ such that the set of all its $m \times n$ windows form a covering code with radius $R$. An upper bound of the smallest array area of an
Externí odkaz:
http://arxiv.org/abs/2404.13674
Recovery sets for vectors and subspaces are important in the construction of distributed storage system codes. These concepts are also interesting in their own right. In this paper, we consider the following very basic recovery question: what is the
Externí odkaz:
http://arxiv.org/abs/2403.20170
Free-space quantum key distribution requires to synchronize the transmitted and received signals. A timing and synchronization system for this purpose based on a de Bruijn sequence has been proposed and studied recently for a channel associated with
Externí odkaz:
http://arxiv.org/abs/2403.01454
One of the primary sequencing methods gaining prominence in DNA storage is nanopore sequencing, attributed to various factors. In this work, we consider a simplified model of the sequencer, characterized as a channel. This channel takes a sequence an
Externí odkaz:
http://arxiv.org/abs/2401.15368