arXiv subjects

Hannah Cuff

Publications and source records attributed to Hannah Cuff.

2 recordsLinked to original sources

arXiv2023

New Qutrit Codes from Pure and Bordered Multidimensional Circulant Construction

We use multidimensional circulant approach to construct new qutrit stabilizer $\dsb{\ell, 0, d}$ codes with parameters $(\ell, d) \in \{(51, 16), (52, 16), (54, 17), (55, 17), (57, 17)\}$ through symplectic self-dual additive codes over $\F_9$. In addition to these five new codes, we use bordered construction to derive two more qutrit codes with parameters $(\ell, d) \in \{(53, 16), (56, 17)\}$ that improve upon previously best known parameters.

cs.IT↗

arXiv2023

New Qubit Codes from Multidimensional Circulant Graphs

Two new qubit stabilizer codes with parameters $[77, 0, 19]_2$ and $[90, 0, 22]_2$ are constructed for the first time by employing additive symplectic self-dual $\F_4$ codes from multidimensional circulant (MDC) graphs. We completely classify MDC graph codes for lengths $4\le n \le 40$ and show that many optimal $\dsb{\ell, 0, d}$ qubit codes can be obtained from the MDC construction. Moreover, we prove that adjacency matrices of MDC graphs have nested block circulant structure and determine isomorphism properties of MDC graphs.

cs.IT↗