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In this paper, we study some codes of algebraic geometry related to certain maximal curves. Quantum stabilizer codes obtained through the self orthogonality of Hermitian codes of this error correcting do not always have good parameters.…

Information Theory · Computer Science 2024-05-07 Behrooz Mosallaei , Farzaneh Ghanbari , Sepideh Farivar , Vahid Nourozi

A simple construction of quaternary hermitian self-orthogonal codes with parameters $[2n+1,k+1]$ and $[2n+2,k+2]$ from a given pair of self-orthogonal $[n,k]$ codes, and its link to quantum codes is considered. As an application, an optimal…

Information Theory · Computer Science 2013-12-10 Vladimir D. Tonchev

Classes of self-dual codes and dual-containing codes are constructed. The codes are obtained within group rings and, using an isomorphism between group rings and matrices, equivalent codes are obtained in matrix form. Distances and other…

Information Theory · Computer Science 2007-11-27 Ted Hurley

For $(n,d)= (66,17),(78,19)$ and $(94,21)$, we construct quantum $[[n,0,d]]$ codes which improve the previously known lower bounds on the largest minimum weights among quantum codes with these parameters. These codes are constructed from…

Combinatorics · Mathematics 2020-11-20 Masaaki Harada

Constacyclic codes are important classes of linear codes that have been applied to the construction of quantum codes. Six new families of asymmetric quantum codes derived from constacyclic codes are constructed in this paper. Moreover, the…

Information Theory · Computer Science 2014-04-01 Liqi Wang , Shixin Zhu

In this paper, we construct the first families of asymmetric quantum convolutional codes (AQCC)'s. These new AQCC's are constructed by means of the CSS-type construction applied to suitable families of classical convolutional codes, which…

Quantum Physics · Physics 2016-10-05 Giuliano G. La Guardia

The stabilizer code is the most general algebraic construction of quantum error-correcting codes proposed so far. A stabilizer code can be constructed from a self-orthogonal subspace of a symplectic space over a finite field. We propose a…

Quantum Physics · Physics 2007-07-13 Ryutaroh Matsumoto

Many $q$-ary stabilizer quantum codes can be constructed from Hermitian self-orthogonal $q^2$-ary linear codes. This result can be generalized to $q^{2 m}$-ary linear codes, $m > 1$. We give a result for easily obtaining quantum codes from…

Information Theory · Computer Science 2024-05-01 Carlos Galindo , Fernando Hernando

In this paper, we construct new families of convolutional codes. Such codes are obtained by means of algebraic geometry codes. Additionally, more families of convolutional codes are constructed by means of puncturing, extending, expanding…

Information Theory · Computer Science 2021-07-27 Francisco Revson F. Pereira , Giuliano G. La Guardia , Francisco M. de Assis

A linear code is said to be self-orthogonal if it is contained in its dual. Self-orthogonal codes are of interest because of their important applications, such as for constructing linear complementary dual (LCD) codes and quantum codes. In…

Information Theory · Computer Science 2023-12-08 Dengcheng Xie , Shixin Zhu , Yang Li

Goyeneche et al recently proposed a notion of orthogonality for quantum Latin squares, and showed that orthogonal quantum Latin squares yield quantum codes. We give a simplified characterization of orthogonality for quantum Latin squares,…

Quantum Physics · Physics 2019-01-30 Benjamin Musto , Jamie Vicary

New infinite families of quantum symmetric and asymmetric codes are constructed. Several of these are MDS. The codes obtained are shown to have parameters which are better than previously known. A number of known codes are special cases of…

Information Theory · Computer Science 2012-08-14 Kenza Guenda , T. Aaron Gulliver

PhD thesis investigating homological quantum codes derived from curved and higher dimensional geometries. In the first part we will consider closed surfaces with constant negative curvature. We show how such surfaces can be constructed and…

Quantum Physics · Physics 2018-02-06 Nikolas P. Breuckmann

Multi-twisted (MT) codes were introduced as a generalization of quasi-twisted (QT) codes. QT codes have been known to contain many good codes. In this work, we show that codes with good parameters and desirable properties can be obtained…

Information Theory · Computer Science 2020-08-18 Nuh Aydin , Thomas Guidotti , Peihan Liu

A curve attaining the Hasse-Weil bound is called a maximal curve. Usually classical error-correcting codes obtained from a maximal curve have good parameters. However, the quantum stabilizer codes obtained from such classical…

Information Theory · Computer Science 2013-11-13 Lingfei Jin

Sarvepalli and Klappenecker showed how classical one-point codes on the Hermitian curve can be used to construct quantum codes. Homma and Kim determined the parameters of a larger family of codes, the two-point codes. In quantum…

Information Theory · Computer Science 2011-02-18 Martianu Frederic Ezerman , Radoslav Kirov

We present new constructions of binary quantum codes from quaternary linear Hermitian self-dual codes. Our main ingredients for these constructions are nearly self-orthogonal cyclic or duadic codes over F_4. An infinite family of…

Information Theory · Computer Science 2022-11-03 Reza Dastbasteh , Petr Lisonek

It is well known that quantum codes can be constructed through classical symplectic self-orthogonal codes. In this paper, we give a kind of Gilbert-Varshamov bound for symplectic self-orthogonal codes first and then obtain the…

Information Theory · Computer Science 2013-08-19 Lingfei Jin , Chaoping Xing

A method of constructing algebraic-geometric codes with many automorphisms arising from Galois points for algebraic curves is presented.

Algebraic Geometry · Mathematics 2022-12-01 Satoru Fukasawa

In this paper, we propose a sufficient condition for a family of 2-generator self-orthogonal quasi-cyclic codes with respect to Hermitian inner product. Supported in the Hermitian construction, we show algebraic constructions of good…

Information Theory · Computer Science 2025-11-25 Liangdong Lu , Gaochi Zhang , Ganyu Feng , Wenzheng Ma