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In order to construct quantum $[[n,0,d]]$ codes for $(n,d)=(56,15)$, $(57,15)$, $(58,16)$, $(63,16)$, $(67,17)$, $(70,18)$, $(71,18)$, $(79,19)$, $(83,20)$, $(87,20)$, $(89,21)$, $(95,20)$, we construct self-dual additive…

Combinatorics · Mathematics 2016-11-16 Markus Grassl , Masaaki Harada

We use symplectic self-dual additive codes over $\mathbb{F}_4$ obtained from metacirculant graphs to construct, for the first time, $[[\ell, 0, d ]]$ qubit codes with parameters $(\ell,d) \in \{(78, 20), (90, 21), (91, 22),…

Information Theory · Computer Science 2021-05-27 Padmapani Seneviratne , Martianus Frederic Ezerman

We introduce quaternary modified four $\mu$-circulant codes as a modification of four circulant codes. We give basic properties of quaternary modified four $\mu$-circulant Hermitian self-dual codes. We also construct quaternary modified…

Information Theory · Computer Science 2024-01-30 Masaaki Harada

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

We introduce a consistent and efficient method to construct self-dual codes over $GF(q)$ with symmetric generator matrices from a self-dual code over $GF(q)$ of smaller length where $q \equiv 1 \pmod 4$. Using this method, we improve the…

Information Theory · Computer Science 2021-02-22 Whan-Hyuk Choi , Jon-Lark Kim

It is well known that quantum codes can be constructed by means of classical symplectic dual-containing codes. This paper considers a family of two-generator quasi-cyclic codes and derives sufficient conditions for these codes to be…

Information Theory · Computer Science 2023-01-09 Chaofeng Guan , Ruihu Li , Liangdong Lu , Yu Yao

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

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

We provide a construction for quantum codes (hermitian-self-orthogonal codes over GF(4)) starting from cyclic codes over GF(4^m). We also provide examples of these codes some of which meet the known bounds for quantum codes.

Quantum Physics · Physics 2007-05-23 Andrew Thangaraj , Steven McLaughlin

This paper presents four new classes of binary quantum codes with minimum dis- tance 3 and 4, namely Class-I, Class-II, Class-III and Class-IV. The classes Class-I and Class-II are constructed based on self-dual orientable embeddings of the…

Quantum Physics · Physics 2015-07-07 Avaz Naghipour , Mohammad Ali Jafarizadeh , Sedaghat Shahmorad

In this paper, we construct self-dual codes from a construction that involves both block circulant matrices and block quadratic residue circulant matrices. We provide conditions when this construction can yield self-dual codes. We construct…

Rings and Algebras · Mathematics 2020-04-02 Joe Gildea , Abidin Kaya , Rhian Taylor , Alexander Tylyshchak , Bahattin Yildiz

We construct qubit stabilizer codes with parameters $[[81, 0, 20]]$ and $[[94, 0, 22]]$ for the first time. We use symplectic self-dual additive codes over $\mathbb{F}_4$ built by modifying the adjacency matrices of suitable metacirculant…

Information Theory · Computer Science 2021-05-28 Padmapani Seneviratne , Martianus Frederic Ezerman

We introduce an altered version of the four circulant construction over group rings for self-dual codes. We consider this construction over the binary field, the rings F_2 + uF_2 and F_4 + uF_4; using groups of order 3, 7, 9, 13, and 15.…

Combinatorics · Mathematics 2019-12-30 Joe Gildea , Abidin Kaya , Alexander Tylyshchak , Bahattin Yildiz

We establish the existence of optimal maximal entanglement entanglement-assisted quantum $[[n,k,d;n-k]]_2$ codes for $(n,k,d)=(14,6,7)$, $(15,7,7)$, $(17,6,9)$, $(17,7,8)$, $(19,7,9)$ and $(20,7,10)$. These codes are obtained from…

Combinatorics · Mathematics 2020-11-20 Masaaki Harada

In this paper, some nonbinary quantum codes using classical codes over Gaussian integers are obtained. Also, some of our quantum codes are better than or comparable with those known before, (for instance [[8; 2; 5]]4+i).

Information Theory · Computer Science 2012-01-16 Murat Güzeltepe , Mehmet Özen

New $s$-extremal extremal unimodular lattices in dimensions $38$, $40$, $42$ and $44$ are constructed from self-dual codes over $\mathbb{F}_5$ by Construction A. In the process of constructing these codes, we obtain a self-dual $[44,22,14]$…

Information Theory · Computer Science 2022-08-09 Masaaki Harada

In this work, we give a new technique for constructing self-dual codes over commutative Frobenius rings using $\lambda$-circulant matrices. The new construction was derived as a modification of the well-known four circulant construction of…

Combinatorics · Mathematics 2021-06-24 Joe Gildea , Adrian Korban , Adam Michael Roberts

In this work, we propose a modified four circulant construction for self-dual codes and a bordered version of the construction using the properties of \lambda-circulant and \lambda-reverse circulant matrices. By using the constructions on…

Information Theory · Computer Science 2016-02-24 Abidin Kaya , Bahattin Yildiz , Abdullah Paşa

In this work, we generalize the four circulant construction for self-dual codes. By applying the constructions over the alphabets F_2, F_2 + uF_2, F_4+uF_4, we were able to obtain extremal binary self-dual codes of lengths 40, 64 including…

Combinatorics · Mathematics 2019-12-30 Joe Gildea , Abidin Kaya , Bahattin Yildiz

In this work, we define a modification of a bordered construction for self-dual codes which utilises $\lambda$-circulant matrices. We provide the necessary conditions for the construction to produce self-dual codes over finite commutative…

Information Theory · Computer Science 2023-01-18 Joe Gildea , Adrian Korban , Adam Michael Roberts , Alexander Tylyshchak
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