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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

In this paper, we study the construction of quantum codes by applying Steane-enlargement to codes from the Hermitian curve. We cover Steane-enlargement of both usual one-point Hermitian codes and of order bound improved Hermitian codes. In…

Information Theory · Computer Science 2020-02-13 René Bødker Christensen , Olav Geil

In this work, we define Generalized Monomial Cartesian Codes (GMCC), which constitute a natural extension of generalized Reed-Solomon codes. We describe how two different generalized Reed-Solomon codes can be combined to construct one GMCC.…

Information Theory · Computer Science 2025-12-19 Oisin Campion , Fernando Hernando , Gary McGuire

Quantum error correction requires the use of error syndromes derived from measurements that may be unreliable. Recently, quantum data-syndrome (QDS) codes have been proposed as a possible approach to protect against both data and syndrome…

Quantum Physics · Physics 2023-02-06 Andrew Nemec

We present several results on quantum codes over general alphabets (that is, in which the fundamental units may have more than 2 states). In particular, we consider codes derived from finite symplectic geometry assumed to have additional…

Quantum Physics · Physics 2007-05-23 Eric M. Rains

We investigate stabilizer codes with carrier qudits of equal dimension $D$, an arbitrary integer greater than 1. We prove that there is a direct relation between the dimension of a qudit stabilizer code and the size of its corresponding…

Quantum Physics · Physics 2015-03-17 Vlad Gheorghiu

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

High-rate bivariate bicycle (BB) codes are promising low-overhead quantum memories, but their stabilizer checks typically have weight $6$ or higher, making syndrome extraction challenging. We introduce subsystem bivariate bicycle (SBB)…

Quantum Physics · Physics 2026-05-07 Zijian Liang , Yu-An Chen

We introduce a class of cyclic quantum codes, basing the construction not on the simplicity of the stabilizers, but rather on the simplicity of preparation of a code state (at least in the absence of noise). We show how certain known codes,…

Quantum Physics · Physics 2025-10-21 Matthew B. Hastings

A divisible binary classical code is one in which every code word has weight divisible by a fixed integer. If the divisor is $2^\nu$ for a positive integer $\nu$, then one can construct a Calderbank-Shor-Steane (CSS) code, where…

Quantum Physics · Physics 2018-04-18 Jeongwan Haah

In this work, we explore a new approach to designing both algorithms and error detection codes for preparing approximate ground states of molecules. We propose a classical algorithm to find the optimal stabilizer state by using excitations…

Quantum Physics · Physics 2025-09-11 Abhinav Anand , Kenneth R. Brown

We introduce a purely graph-theoretical object, namely the coding clique, to construct quantum errorcorrecting codes. Almost all quantum codes constructed so far are stabilizer (additive) codes and the construction of nonadditive codes,…

Quantum Physics · Physics 2007-09-13 Sixia Yu , Qing Chen , C. H. Oh

We establish a database consisting of a representative of every binary quantum stabilizer code under local Clifford permutation equivalence for $n\leq 9$.

Quantum Physics · Physics 2025-01-30 Andrew Cross , Drew Vandeth

Clifford codes can be understood as a generalization of stabilizer codes. To show the existence of a true Clifford code which is better than any stabilizer code is a well known open problem in the theory of Clifford codes. One of the main…

Quantum Physics · Physics 2007-05-23 Hagiwara Manabu , Hideki Imai

We introduce multivariate multicycle (MM) codes, a new family of quantum error-correcting codes (QECCs) that unifies bivariate bicycle, multivariate bicycle, abelian two-block group algebra, generalized bicycle, trivariate tricycle, and…

Quantum Physics · Physics 2026-05-26 Feroz Ahmed Mian , Owen Gwilliam , Stefan Krastanov

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

The entanglement-assisted stabilizer formalism can transform arbitrary classical linear codes into entanglement-assisted quantum error correcting codes (EAQECCs). In this work, we construct some new entanglement-assisted quantum MDS…

Information Theory · Computer Science 2019-11-20 Shixin Zhu , Wan Jiang , Xiaojing Chen

A class of powerful $q$-ary linear polynomial codes originally proposed by Xing and Ling is deployed to construct good asymmetric quantum codes via the standard CSS construction. Our quantum codes are $q$-ary block codes that encode $k$…

Information Theory · Computer Science 2016-04-18 Martianus Frederic Ezerman , Somphong Jitman , Patrick Solé

We formulate a bounded distance decoding strategy applicable to all stabilizer codes including both CSS and non-CSS code-families. The framework emerges out of the local Clifford equivalence between arbitrary stabilizer states and graph…

Quantum Physics · Physics 2026-04-29 Harikrishnan K J , Amit Kumar Pal

We construct a quantum low-density parity-check code family from a length-$512$ Calderbank--Shor--Steane base matrix pair. The base pair is permutation-equivalent to the known SPC(3) product CSS code, and the present affine-coset…

Quantum Physics · Physics 2026-04-27 Koki Okada , Kenta Kasai