Zobrazeno 1 - 10
of 581
pro vyhledávání: '"ling, San"'
Finding a mass formula for a given class of linear codes is a fundamental problem in combinatorics and coding theory. In this paper, we consider the action of the unitary (resp. symplectic) group on the set of all Hermitian (resp. symplectic) linear
Externí odkaz:
http://arxiv.org/abs/2410.13578
Quasi-twisted codes are used here as the classical ingredients in the so-called Construction X for quantum error-control codes. The construction utilizes nearly self-orthogonal codes to design quantum stabilizer codes. We expand the choices of the in
Externí odkaz:
http://arxiv.org/abs/2405.15057
Hermitian hulls of linear codes are interesting for theoretical and practical reasons alike. In terms of recent application, linear codes whose hulls meet certain conditions have been utilized as ingredients to construct entanglement-assisted quantum
Externí odkaz:
http://arxiv.org/abs/2404.04993
The $b$-symbol metric is a generalization of the Hamming metric. Linear codes, in the $b$-symbol metric, have been used in the read channel whose outputs consist of $b$ consecutive symbols. The Griesmer bound outperforms the Singleton bound for $\mat
Externí odkaz:
http://arxiv.org/abs/2401.04941
Classical locally recoverable codes (LRCs) have become indispensable in distributed storage systems. They provide efficient recovery in terms of localized errors. Quantum LRCs have very recently been introduced for their potential application in quan
Externí odkaz:
http://arxiv.org/abs/2312.11115
The existence of $q$-ary linear complementary pairs (LCPs) of codes with $q> 2$ has been completely characterized so far. This paper gives a characterization for the existence of binary LCPs of codes. As a result, we solve an open problem proposed by
Externí odkaz:
http://arxiv.org/abs/2312.09482
Spectral bounds form a powerful tool to estimate the minimum distances of quasi-cyclic codes. They generalize the defining set bounds of cyclic codes to those of quasi-cyclic codes. Based on the eigenvalues of quasi-cyclic codes and the corresponding
Externí odkaz:
http://arxiv.org/abs/2311.08156
A coded distributed computing (CDC) system aims to reduce the communication load in the MapReduce framework. Such a system has $K$ nodes, $N$ input files, and $Q$ Reduce functions. Each input file is mapped by $r$ nodes and each Reduce function is co
Externí odkaz:
http://arxiv.org/abs/2309.04305
Coded distributed computing (CDC) was introduced to greatly reduce the communication load for MapReduce computing systems. Such a system has $K$ nodes, $N$ input files, and $Q$ Reduce functions. Each input file is mapped by $r$ nodes and each Reduce
Externí odkaz:
http://arxiv.org/abs/2307.04209
Autor:
Kruglik, Stanislav, Luo, Gaojun, Kim, Wilton, Singhvi, Shubhransh, Kiah, Han Mao, Ling, San, Wang, Huaxiong
We consider the repair scheme of Guruswami-Wootters for the Reed-Solomon code and ask: can we correctly repair a failed node in the presence of erroneous nodes? Equivalently, we consider the collection of downloaded traces as a code and investigate i
Externí odkaz:
http://arxiv.org/abs/2305.03442