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Related papers: Constructions of q-Ary Constant-Weight Codes

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The sizes of optimal constant-composition codes of weight three have been determined by Chee, Ge and Ling with four cases in doubt. Group divisible codes played an important role in their constructions. In this paper, we study the problem…

Information Theory · Computer Science 2014-10-03 Wei Hengjia , Zhang Hui , Zhu Mingzhi , Ge Gennian

Combinatorial designs are closely related to linear codes. In recent year, there are a lot of $t$-designs constructed from certain linear codes. In this paper, we aim to construct $2$-designs from binary three-weight codes. For any binary…

Information Theory · Computer Science 2023-12-22 Canze Zhu , Qunying Liao , Haibo Liu

We introduce the class of multiply constant-weight codes to improve the reliability of certain physically unclonable function (PUF) response. We extend classical coding methods to construct multiply constant-weight codes from known $q$-ary…

Information Theory · Computer Science 2014-01-17 Yeow Meng Chee , Zouha Cherif , Jean-Luc Danger , Sylvain Guilley , Han Mao Kiah , Jon-Lark Kim , Patrick Solé , Xiande Zhang

A $q$-ary code $C$ of length $n$ is a set of $n$-dimensional vectors (code words) with entries in $\{0, \ldots, q-1\}$. We say $C$ has constant weight $w$ if each code word has exactly $w$ nonzero entries. We say $C$ has minimum distance…

Combinatorics · Mathematics 2024-11-26 Patrick Bennett

Linear codes with a few weights can be applied to secrete sharing, authentication codes, association schemes and strongly regular graphs. For an odd prime power $q$, we construct a class of three-weight $\F_q$-linear codes from quadratic…

Information Theory · Computer Science 2024-10-04 Xiumei Li , Zongxi Chen , Fei Li

We explicitly construct an infinite family of asymptotically good concatenated quantum stabilizer codes where the outer code uses CSS-type quantum Reed-Solomon code and the inner code uses a set of special quantum codes. In the field of…

Quantum Physics · Physics 2009-01-06 Zhuo Li , Li-Juan Xing , Xin-Mei Wang

Linear codes have been an interesting topic in both theory and practice for many years. In this paper, a class of $q$-ary linear codes with few weights are presented and their weight distributions are determined using Gauss periods. Some of…

Information Theory · Computer Science 2018-11-26 Gaopeng Jian

A new method to construct $q$-ary complementary sequence (or array) sets (CSSs) and complete complementary codes (CCCs) of size $N$ is introduced in this paper. An algorithm on how to compute the explicit form of the functions in…

Information Theory · Computer Science 2020-05-13 Zilong Wang , Dongxu Ma , Guang Gong

A conflict-avoiding code (CAC) is a deterministic transmission scheme for asynchronous multiple access without feedback. When the number of simultaneously active users is less than or equal to $w$, a CAC of length $L$ with weight $w$ can…

Information Theory · Computer Science 2024-12-17 Yuan-Hsun Lo , Tsai-Lien Wong , Kangkang Xu , Yijin Zhang

Using the notion of generalized weight we improve estimates on the parameters of quantum codes obtained by Steane's construction from binary codes. This yields several new families of quantum codes.

Quantum Physics · Physics 2007-05-23 Gérard Cohen , Sylvia Encheva , Simon Litsyn

Quaternary code (QC) designs form an attractive class of nonregular factorial fractions. We develop a complementary set theory for characterizing optimal QC designs that are highly fractionated in the sense of accommodating a large number…

Statistics Theory · Mathematics 2013-12-19 Rahul Mukerjee , Boxin Tang

This paper provides new constructive lower bounds for constant dimension codes, using different techniques such as Ferrers diagram rank metric codes and pending blocks. Constructions for two families of parameters of constant dimension…

Information Theory · Computer Science 2014-09-03 Natalia Silberstein , Anna-Lena Trautmann

Many $q$-ary stabilizer quantum codes can be constructed from Hermitian self-orthogonal $q^2$-ary linear codes. This result can be generalized to $q^{2 m}$-ary linear codes, $m > 1$. We give a result for easily obtaining quantum codes from…

Information Theory · Computer Science 2024-05-01 Carlos Galindo , Fernando Hernando

In this paper, we mainly study quaternary linear codes and their binary subfield codes. First we obtain a general explicit relationship between quaternary linear codes and their binary subfield codes in terms of generator matrices and…

Information Theory · Computer Science 2022-01-03 Yansheng Wu , Chengju Li , Fu Xiao

A constant weight binary code consists of $n$-bit binary codewords, each with exactly $w$ bits equal to 1, such that any two codewords are at least Hamming distance $d$ apart. $A(n,d,w)$ is the maximum size of a constant weight binary code…

Information Theory · Computer Science 2026-03-03 Christopher D. Rosin

This paper computationally obtains optimal bounded-weight, binary, error-correcting codes for a variety of distance bounds and dimensions. We compare the sizes of our codes to the sizes of optimal constant-weight, binary, error-correcting…

Information Theory · Computer Science 2007-10-15 Russell Bent , Michael Schear , Lane A. Hemaspaandra , Gabriel Istrate

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 new method of constructing optimum constant weight codes over F_2 based on a generalized $(u, u+v)$ construction is presented. We present a new method of constructing superimposed code $C_{(s_1,s_2,\cdots,s_I)}^{(h_1, h_2, \cdots, h_I)}$…

Information Theory · Computer Science 2014-06-24 Masao Kasahara , Shigeichi Hirasawa

We construct a class of three-Lee-weight and two infinite families of five-Lee-weight codes over the ring $R=\mathbb{F}_2 +v\mathbb{F}_2 +v^2\mathbb{F}_2 +v^3\mathbb{F}_2 +v^4\mathbb{F}_2,$ where $v^5=1.$ The same ring occurs in the quintic…

Information Theory · Computer Science 2017-01-05 Yan Liu , Minjia Shi , Patrick Solé

We demonstrate that certain Johnson-type bounds are asymptotically exact for a variety of classes of codes, namely, constant-composition codes, nonbinary constant-weight codes and multiply constant-weight codes. This was achieved via an…

Combinatorics · Mathematics 2014-01-21 Yeow Meng Chee , Fei Gao , Han Mao Kiah , Alan Chi Hung Ling , Hui Zhang , Xiande Zhang