Zobrazeno 1 - 10
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pro vyhledávání: '"Matthews, Gretchen L"'
The Generalized Hamming weights and their relative version, which generalize the minimum distance of a linear code, are relevant to numerous applications, including coding on the wire-tap channel of type II, $t$-resilient functions, bounding the card
Externí odkaz:
http://arxiv.org/abs/2411.13375
Autor:
Matthews, Gretchen L, McMillon, Emily
Bit Flipping Key Encapsulation (BIKE) is a code-based cryptosystem being considered in Round 4 of the NIST Post-Quantum Cryptography Standardization process. It is based on quasi-cyclic moderate-density parity-check (QC-MDPC) codes paired with an ite
Externí odkaz:
http://arxiv.org/abs/2410.11111
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