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Quadratic residue codes have been one of the most important classes of algebraic codes. They have been generalized into duadic codes and quadratic double circulant codes. In this paper we introduce a new subclass of double circulant codes,…

Information Theory · Computer Science 2012-02-07 Sunghyu Han , Jon-Lark Kim

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

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

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 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 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

In the field of algebraic geometric codes (AG codes), the characterization of dual codes has long been a challenging problem which relies on differentials. In this paper, we provide some descriptions for certain differentials utilizing…

Information Theory · Computer Science 2025-01-29 Puyin Wang , Jinquan Luo

There have been various constructions of classical codes from polynomial valuations in literature \cite{ARC04, LNX01,LX04,XF04,XL00}. In this paper, we present a construction of classical codes based on polynomial construction again. One of…

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

Linear complementary dual codes (or codes with complementary duals) are codes whose intersections with their dual codes are trivial. We study the largest minimum weight $d(n,k)$ among all binary linear complementary dual $[n,k]$ codes. We…

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

In this paper, constructions of some double circulant self-dual codes by generalized cyclotomic classes of order two are presented. This technique is applied to [72, 36, 12] binary highest know self-dual codes to obtain self-dual codes over…

Information Theory · Computer Science 2019-12-16 Wenpeng Gao , Tongjiang Yan

The problem of finding quantum error-correcting codes is transformed into the problem of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product. Many new codes and new bounds are…

Quantum Physics · Physics 2008-02-03 A. R. Calderbank , E. M Rains , P. W. Shor , N. J. A. Sloane

We give two methods for constructing many linear complementary dual (LCD for short) codes from a given LCD code, by modifying some known methods for constructing self-dual codes. Using the methods, we construct binary LCD codes and…

Information Theory · Computer Science 2021-01-29 Masaaki Harada

Due to their fast decoding algorithms, quantum generalizations of low-density parity check, or LDPC, codes have been investigated as a solution to the problem of decoherence in fragile quantum states. However, the additional twisted inner…

Quantum Physics · Physics 2012-07-04 Jacob Farinholt

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

We study additive quaternary codes whose parameters are close to those of the extended cyclic [12; 6; 6]4-code or to the quaternary linear codes generated by the elliptic quadric in PG(3; 4) or its dual. In particular we characterize those…

Combinatorics · Mathematics 2018-04-10 Juergen Bierbrauer , Stefano Marcugini , Fernanda Pambianco

In this work, we apply the idea of composite matrices arising from group rings to derive a number of different techniques for constructing self-dual codes over finite commutative Frobenius rings. By applying these techniques over different…

Combinatorics · Mathematics 2023-01-18 Joe Gildea , Adrian Korban , Adam Michael Roberts

Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. It is very hard to construct quantum MDS codes with relatively large minimum distance. In this paper, based on classical constacyclic codes, we…

Information Theory · Computer Science 2014-05-22 Liqi Wang , Shixin Zhu

We present a general construction of asymmetric quantum codes based on additive codes under the trace Hermitian inner product. Various families of additive codes over $\F_{4}$ are used in the construction of many asymmetric quantum codes…

Information Theory · Computer Science 2013-07-04 Martianus Frederic Ezerman , San Ling , Patrick Sole

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

One central theme in quantum error-correction is to construct quantum codes that have a large minimum distance. In this paper, we first present a construction of classical codes based on certain class of polynomials. Through these classical…

Information Theory · Computer Science 2015-08-06 Tao Zhang , Gennian Ge