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Related papers: New quantum codes from self-dual codes over F_4

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In this paper, we provide two methods of constructing quantum codes from linear codes over finite chain rings. The first one is derived from the Calderbank-Shor-Steane (CSS) construction applied to self-dual codes over finite chain rings.…

Information Theory · Computer Science 2017-04-24 Xiusheng Liu , Hualu Liu

A new bound on the minimum distance of q-ary cyclic codes is proposed. It is based on the description by another cyclic code with small minimum distance. The connection to the BCH bound and the Hartmann--Tzeng (HT) bound is formulated…

Information Theory · Computer Science 2012-09-03 Alexander Zeh , Sergey Bezzateev

This article studies one-generator and two-generator quasi-cyclic codes over finite fields. We present two versions of necessary and sufficient conditions for the symplectic selforthogonality of one-generator quasi-cyclic codes, using both…

Information Theory · Computer Science 2024-12-19 Tushar Bag , Hai Q Dinh , Daniel Panario

Binary cyclic codes are worth studying due to their applications and theoretical importance. It is an important problem to construct an infinite family of cyclic codes with large minimum distance $d$ and dual distance $d^{\perp}$. In recent…

Information Theory · Computer Science 2026-04-14 Lingqi Zheng , Weijun Fang , Rongxing Qiu

Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Inspired by the recent work on binary cyclic codes published in…

Information Theory · Computer Science 2023-05-03 Tingfang Chen , Cunsheng Ding , Chengju Li , Zhonghua Sun

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

Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, monomials and trinomials over…

Information Theory · Computer Science 2013-10-08 Cunsheng Ding , Zhengchun Zhou

In this paper, we present three new classes of $q$-ary quantum MDS codes utilizing generalized Reed-Solomon codes satisfying Hermitian self-orthogonal property. Among our constructions, the minimum distance of some $q$-ary quantum MDS codes…

Information Theory · Computer Science 2019-09-18 Xiaolei Fang , Jinquan Luo

This paper gives new methods of constructing {\it symmetric self-dual codes} over a finite field $GF(q)$ where $q$ is a power of an odd prime. These methods are motivated by the well-known Pless symmetry codes and quadratic double circulant…

Information Theory · Computer Science 2021-02-18 Whan-Hyuk Choi , Jon-Lark Kim

In this article, we construct infinite families of quaternary (that is, over the ring $\mathbb{Z}_4$) $\mathcal{C}_{D}$-codes, where the defining set $D$ is derived utilizing a two-generator simplicial complex, and determine their Lee…

Information Theory · Computer Science 2026-05-15 Ankit Yadav , Nilay Kumar Mondal , Ritumoni Sarma

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

Duadic codes are a class of cyclic codes that generalizes quadratic residue codes from prime to composite lengths. For every prime power q, we characterize the integers n such that over the finite field with q^2 elements there is a duadic…

Combinatorics · Mathematics 2007-05-23 Lilibeth Dicuangco , Pieter Moree , Patrick Sole

We consider quantum MDS (QMDS) codes for quantum systems of dimension $q$ with lengths up to $q^2+2$ and minimum distances up to $q+1$. We show how starting from QMDS codes of length $q^2+1$ based on cyclic and constacyclic codes, new QMDS…

Quantum Physics · Physics 2016-01-25 Markus Grassl , Martin Roetteler

We study the construction of quasi-cyclic self-dual codes, especially of binary cubic ones. We consider the binary quasi-cyclic codes of length 3\ell with the algebraic approach of [9]. In particular, we improve the previous results by…

Number Theory · Mathematics 2017-06-26 Pınar Çomak , Jon-Lark Kim , Ferruh Özbudak

In this work, we introduce new construction methods for self-dual codes using a Baumert-Hall array. We apply the constructions over the alphabets F_2 and F_4 + uF_4 and combine them with extension theorems and neighboring constructions. As…

Combinatorics · Mathematics 2019-02-06 Abidin Kaya , 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

The largest minimum weights among quaternary Hermitian linear complementary dual codes are known for dimension $2$. In this paper, we give some conditions for the nonexistence of quaternary Hermitian linear complementary dual codes with…

Combinatorics · Mathematics 2020-11-20 Makoto Araya , Masaaki Harada , Ken Saito

We present new quantum codes with good parameters which are constructed from self-orthogonal algebraic geometry codes. Our method permits a wide class of curves to be used in the formation of these codes, which greatly extends the class of…

Algebraic Geometry · Mathematics 2025-01-17 Fernando Hernando , Gary McGuire , Francisco Monserrat , Julio José Moyano-Fernández

We construct MDS Euclidean and Hermitian self-dual codes over large finite fields of odd and even characteristics. Our codes arise from cyclic and negacyclic duadic codes.

Information Theory · Computer Science 2010-04-08 Kenza Guenda

Self-dual codes have been studied actively because they are connected with mathematical structures including block designs and lattices and have practical applications in quantum error-correcting codes and secret sharing schemes.…

Cryptography and Security · Computer Science 2024-09-04 Minjia Shi , Sihui Tao , Jihoon Hong , Jon-Lark Kim
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