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Computer Science > Information Theory

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By Martianus Frederic
| arxiv.org
We prove that any generalized extended code is monomially equivalent to the Hermitian dual of a code which is closely related to a second kind of extended code of $\C^{\perp_{\rm H}}$. Every $[n+1,k+1]_{q^2}$ linear code $\D$ with $d(\D^{\perp_{\rm H}})>1$ is monomially equivalent to the generalized extended code $\C({\bf u},a)$ of an $[n,k]_{q^2}$ linear code $\C$ for a fixed $a\in\F_{q^2}^{*}$ and some ${\bf u}\in\F_{q^2}^{n}$.
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[2512.17128] Hermitian Hulls of Rational Algebraic Geometry Codes and Applications in Quantum Codes

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By Martianus Frederic
| arxiv.org
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
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[2405.15057] Characterization of Nearly Self-Orthogonal Quasi-Twisted Codes and Related Quantum Codes

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By Martianus Frederic, Markus Grassl, San Ling, Ferruh Özbudak
| arxiv.org
[Submitted on 23 May 2024 ( v1 ), last revised 6 Sep 2024 (this version, v2)] Title:Characterization of Nearly Self-Orthogonal Quasi-Twisted Codes and Related Quantum Codes View a PDF of the paper titled Characterization of Nearly Self-Orthogonal Quasi-Twisted Codes and Related Quantum Codes, by Martianus Frederic Ezerman and 4 other authors View PDF HTML (experimental) Abstract:Quasi-twisted codes are used here as the classical ingredients in the so-called Construction X for quantum...
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