Binary optimal linear codes with various hull dimensions and entanglement-assisted QECC

DOI10.1007/S40314-023-02268-ZarXiv2210.14549MaRDI QIDQ6415173

Author name not available (Why is that?)

Publication date: 26 October 2022

Abstract: The hull of a linear code $C$ is the intersection of $C$ with its dual. To the best of our knowledge, there are very few constructions of binary linear codes with the hull dimension $ge2$ except for self-orthogonal codes. We propose a building-up construction to obtain a plenty of binary $[n+2,k+1]$ codes with hull dimension $ell,ell+1$, or $ell+2$ from a given binary $[n,k]$ code with hull dimension $ell$. In particular, with respect to hull dimensions 1 and 2, we construct all binary optimal $[n,k]$ codes of lengths up to 13. With respect to hull dimensions 3, 4, and 5, we construct all binary optimal $[n,k]$ codes of lengths up to 12 and the best possible minimum distances of $[13,k]$ codes for $3lekle10$. As an application, we apply our binary optimal codes with a given hull dimension to construct several entanglement-assisted quantum error-correcting codes(EAQECC) with the best known parameters.

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