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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

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 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

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

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

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…

Information Theory · Computer Science 2023-09-06 Padmapani Seneviratne , Hannah Cuff , Alexandra Koletsos , Kerry Seekamp , Adrian Thnanopavarn

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 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

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

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

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

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 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

We show that (n,2^n) additive codes over GF(4) can be represented as directed graphs. This generalizes earlier results on self-dual additive codes over GF(4), which correspond to undirected graphs. Graph representation reduces the…

Combinatorics · Mathematics 2011-03-17 Lars Eirik Danielsen , Matthew G. Parker

In this work, quadratic double and quadratic bordered double circulant constructions are applied to F_4 + uF_4 as well as F_4, as a result of which extremal binary self-dual codes of length 56 and 64 are obtained. The binary extension…

Combinatorics · Mathematics 2016-02-25 Abidin Kaya , Bahattin Yildiz , Irfan Siap

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

In this work, connected cubic planar bipartite graphs and related binary self-dual codes are studied. Binary self-dual codes of length 16 are obtained by face-vertex incidence matrices of these graphs. By considering their lifts to the ring…

Combinatorics · Mathematics 2016-10-04 Abidin Kaya

In this work, four circulant and quadratic double circulant (QDC) constructions are applied to the family of the rings R_k,m. Self-dual binary codes are obtained as the Gray images of self-dual QDC codes over R_k,m. Extremal binary…

Information Theory · Computer Science 2016-10-31 Abidin Kaya , Nesibe Tüfekçi

In this paper, we present a new bordered construction for self-dual codes which employs $\lambda$-circulant matrices. We give the necessary conditions for our construction to produce self-dual codes over a finite commutative Frobenius ring…

Information Theory · Computer Science 2023-03-24 Joe Gildea , Adrian Korban , Adam Michael Roberts , Alexander Tylyshchak

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…

Information Theory · Computer Science 2023-12-21 Padmapani Seneviratne , Hannah Cuff , Alexandra Koletsos , Kerry Seekamp , Adrian Thananopavarn
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