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A basic problem for constant dimension codes is to determine the maximum possible size $A_q(n,d;k)$ of a set of $k$-dimensional subspaces in $\mathbb{F}_q^n$, called codewords, such that the subspace distance satisfies…

Information Theory · Computer Science 2022-12-22 Sascha Kurz

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

Conflict-avoiding codes are used in the multiple-access collision channel without feedback. The number of codewords in a conflict-avoiding code is the number of potential users that can be supported in the system. In this paper, a new upper…

Information Theory · Computer Science 2010-11-09 Kenneth W. Shum , Wing Shing Wong , Chung Shue Chen

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

One of the most fundamental topics in subspace coding is to explore the maximal possible value ${\bf A}_q(n,d,k)$ of a set of $k$-dimensional subspaces in $\mathbb{F}_q^n$ such that the subspace distance satisfies $\operatorname{d_S}(U,V) =…

Information Theory · Computer Science 2021-03-19 Xianmang He , Yindong Chen , Zusheng Zhang , Kunxiao Zhou

In \cite{shi2022few-weight}, Shi and Li studied $\mathcal{C}_D$-codes over the ring $\mathcal{R}:=\mathbb{F}_2[x,y]/\langle x^2, y^2, xy-yx\rangle$ and their binary Gray images, where $D$ is derived using certain simplicial complexes. We…

Information Theory · Computer Science 2025-10-13 Ankit Yadav , Ritumoni Sarma , Anuj Kumar Bhagat

A weighing matrix $W$ of order $n=\frac{p^{m+1}-1}{p-1}$ and weight $p^m$ is constructed and shown that the rows of $W$ and $-W$ form optimal constant weight ternary codes of length $n$, weight $p^m$ and minimum distance…

Combinatorics · Mathematics 2021-12-09 Hadi Kharaghani , Sho Suda , Vlad Zaitsev

We propose a method for a classification of quaternary Hermitian LCD codes having large minimum weights. As an example, we give a classification of quaternary optimal Hermitian LCD codes of dimension 3.

Information Theory · Computer Science 2021-09-24 Makoto Araya , Masaaki Harada

The additive codes may have better parameters than linear codes. However, it is still a challenging problem to efficiently construct additive codes that outperform linear codes, especially those with greater distances than linear codes of…

Information Theory · Computer Science 2023-06-22 Chaofeng Guan , Ruihu Li , Yiting Liu , Zhi Ma

We consider the weight spectrum of a class of quasi-perfect binary linear codes with code distance 4. For example, extended Hamming code and Panchenko code are the known members of this class. Also, it is known that in many cases Panchenko…

Information Theory · Computer Science 2017-06-13 Valentine B. Afanassiev , Alexander A. Davydov

In this letter we consider the ensemble of codes formed by the serial concatenation of a Hamming code and two accumulate codes. We show that this ensemble is asymptotically good, in the sense that most codes in the ensemble have minimum…

Information Theory · Computer Science 2009-05-29 Alexandre Graell i Amat , Raphael Le Bidan

For the past decades, linear codes with few weights have been widely studied, since they have applications in space communications, data storage and cryptography. In this paper, a class of binary linear codes is constructed and their weight…

Information Theory · Computer Science 2016-02-03 Fei Li , Yang Yan , Qiuyan Wang , Tongjiang Yan

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

Diameter perfect codes form a natural generalization for perfect codes. They are based on the code-anticode bound which generalizes the sphere-packing bound. The code-anticode bound was proved by Delsarte for distance-regular graphs and it…

Information Theory · Computer Science 2021-09-28 Tuvi Etzion

It is reasonable to expect the theory of quantum codes to be simplified in the case of codes of minimum distance 2; thus, it makes sense to examine such codes in the hopes that techniques that prove effective there will generalize. With…

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

A family of $\omega$-circulant balanced weighing matrices with classical parameters is used for the construction of optimal constant weight codes over an alphabet of size $g+1$ and length $n=(q^m -1)/(q-1)$, where $q$ is an odd prime power,…

Combinatorics · Mathematics 2023-07-26 Hadi Kharaghani , Thomas Pender , Vladimir D. Tonchev

Subspace codes have important applications in random network coding. It is interesting to construct subspace codes with both sizes, and the minimum distances are as large as possible. In particular, cyclic constant dimension subspaces codes…

Information Theory · Computer Science 2023-05-24 Yun Li , Hongwei Liu , Sihem Mesnager

Based on the generic construction of linear codes, we construct linear codes over the ring $\Bbb Z_4$ via posets of the disjoint union of two chains. We determine the Lee weight distributions of the quaternary codes. Moreover, we obtain…

Information Theory · Computer Science 2019-10-29 Xiaomeng Zhu , Yansheng Wu , Qin Yue

A class of optimal three-weight cyclic codes of dimension 3 over any finite field was presented by Vega [Finite Fields Appl., 42 (2016) 23-38]. Shortly thereafter, Heng and Yue [IEEE Trans. Inf. Theory, 62(8) (2016) 4501-4513] generalized…

Information Theory · Computer Science 2021-07-12 Gerardo Vega , Félix Hernández

Constructions of distance-optimal codes and quasi-perfect codes are challenging problems and have attracted many attentions. In this paper, we give the following three results. 1) If $\lambda|q^{sm}-1$ and $\lambda…

Information Theory · Computer Science 2024-02-16 Hao Chen