Zobrazeno 1 - 10
of 146
pro vyhledávání: '"Matthews, Gretchen"'
Autor:
Camps-Moreno, Eduardo, López, Hiram H., Matthews, Gretchen L., Ruano, Diego, San-José, Rodrigo, Soprunov, Ivan
In this paper, we study binary triorthogonal codes and their relation to CSS-T quantum codes. We characterize the binary triorthogonal codes that are minimal or maximal with respect to the CSS-T poset, and we also study how to derive new triorthogona
Externí odkaz:
http://arxiv.org/abs/2408.02916
CSS-T codes were recently introduced as quantum error-correcting codes that respect a transversal gate. A CSS-T code depends on a pair $(C_1, C_2)$ of binary linear codes $C_1$ and $C_2$ that satisfy certain conditions. We prove that $C_1$ and $C_2$
Externí odkaz:
http://arxiv.org/abs/2406.00425
Autor:
Matthews, Gretchen L., Soto, Pedro
We extend coded distributed computing over finite fields to allow the number of workers to be larger than the field size. We give codes that work for fully general matrix multiplication and show that in this case we serendipitously have that all func
Externí odkaz:
http://arxiv.org/abs/2405.09746
In this paper, we study algebraic geometry codes from curves over $\mathbb{F}_{q^\ell}$ through their virtual projections which are algebraic geometric codes over $\mathbb{F}_q$. We use the virtual projections to provide fractional decoding algorithm
Externí odkaz:
http://arxiv.org/abs/2404.07201
Autor:
Camps-Moreno, Eduardo, López, Hiram H., Matthews, Gretchen L., Ruano, Diego, San-José, Rodrigo, Soprunov, Ivan
Publikováno v:
Quantum Inf Process 23, 230 (2024)
CSS-T codes were recently introduced as quantum error-correcting codes that respect a transversal gate. A CSS-T code depends on a CSS-T pair, which is a pair of binary codes $(C_1, C_2)$ such that $C_1$ contains $C_2$, $C_2$ is even, and the shorteni
Externí odkaz:
http://arxiv.org/abs/2312.17518
Employing underlying geometric and algebraic structures allows for constructing bespoke codes for local recovery of erasures. We survey techniques for enriching classical codes with additional machinery, such as using lines or curves in projective sp
Externí odkaz:
http://arxiv.org/abs/2312.16314
Codes with locality, also known as locally recoverable codes, allow for recovery of erasures using proper subsets of other coordinates. Theses subsets are typically of small cardinality to promote recovery using limited network traffic and other reso
Externí odkaz:
http://arxiv.org/abs/2310.20533
Binary codes of length $n$ may be viewed as subsets of vertices of the Boolean hypercube $\{0,1\}^n$. The ability of a linear error-correcting code to recover erasures is connected to influences of particular monotone Boolean functions. These functio
Externí odkaz:
http://arxiv.org/abs/2308.01781
In this paper, we introduce curve-lifted codes over fields of arbitrary characteristic, inspired by Hermitian-lifted codes over $\mathbb{F}_{2^r}$. These codes are designed for locality and availability, and their particular parameters depend on the
Externí odkaz:
http://arxiv.org/abs/2307.13183
We investigate adversarial network coding and decoding focusing on the multishot regime. Errors can occur on a proper subset of the network edges and are modeled via an adversarial channel. The paper contains both bounds and capacity-achieving scheme
Externí odkaz:
http://arxiv.org/abs/2307.08839