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In this paper, we construct a large family of projective linear codes over ${\mathbb F}_{q}$ from the general simplicial complexes of ${\mathbb F}_{q}^m$ via the defining-set construction, which generalizes the results of [IEEE Trans. Inf.…

Information Theory · Computer Science 2023-05-15 Zhao Hu , Yunge Xu , Nian Li , Xiangyong Zeng , Lisha Wang , Xiaohu Tang

A conjugate code pair is defined as a pair of linear codes either of which contains the dual of the other. A conjugate code pair represents the essential structure of the corresponding Calderbank-Shor-Steane (CSS) quantum error-correcting…

Information Theory · Computer Science 2007-07-13 Mitsuru Hamada

We show how good quantum error-correcting codes can be constructed using generalized concatenation. The inner codes are quantum codes, the outer codes can be linear or nonlinear classical codes. Many new good codes are found, including both…

Quantum Physics · Physics 2010-06-01 Markus Grassl , Peter W. Shor , Bei Zeng

Inspired by the Z2Z4-additive codes, linear codes over Z2^r x(Z2+uZ2)^s have been introduced by Aydogdu et al. more recently. Although these family of codes are similar to each other, linear codes over Z2^r x(Z2+uZ2)^s have some advantages…

Information Theory · Computer Science 2017-04-25 Ismail Aydogdu

The paper deals with the perfect 1-error correcting codes over a finite field with $q$ elements (briefly $q$-ary 1-perfect codes). We show that the orthogonal code to the $q$-ary non-full-rank 1-perfect code of length $n = (q^{m}-1)/(q-1)$…

Information Theory · Computer Science 2017-04-11 Alexander M. Romanov

Recently, constructions of optimal linear codes from simplicial complexes have attracted much attention and some related nice works were presented. Let $q$ be a prime power. In this paper, by using the simplicial complexes of ${\mathbb…

Information Theory · Computer Science 2024-07-16 Bing Chen , Yunge Xu , Zhao Hu , Nian Li , Xiangyong Zeng

Recently, Chang and Hyun obtained some classes of binary optimal codes via simplicial complexes. In this letter, we utilize posets of the disjoint union of two chains to construct binary optimal linear codes.

Information Theory · Computer Science 2019-07-01 Yansheng Wu , Jong Yoon Hyun , Qin Yue

Pairwise disjoint 3-GDDs can be used to construct some optimal constant-weight codes. We study the existence of a pair of disjoint 3-GDDs of type $g^t u^1$ and establish that its necessary conditions are also sufficient.

Combinatorics · Mathematics 2010-08-27 Yanxun Chang , Yeow Meng Chee , Junling Zhou

Constant-dimension codes have recently received attention due to their significance to error control in noncoherent random network coding. In this paper, we show that constant-rank codes are closely related to constant-dimension codes and…

Information Theory · Computer Science 2008-05-07 Maximilien Gadouleau , Zhiyuan Yan

We introduce a consistent and efficient method to construct self-dual codes over $GF(q)$ with symmetric generator matrices from a self-dual code over $GF(q)$ of smaller length where $q \equiv 1 \pmod 4$. Using this method, we improve the…

Information Theory · Computer Science 2021-02-22 Whan-Hyuk Choi , Jon-Lark Kim

A generic construction of linear codes over finite fields has recently received a lot of attention, and many one-weight, two-weight and three-weight codes with good error correcting capability have been produced with this generic approach.…

Information Theory · Computer Science 2015-12-23 Can Xiang

In 'An asymptotic result on compressed sensing matrices', a new construction for compressed sensing matrices using combinatorial design theory was introduced. In this paper, we use deterministic and probabilistic methods to analyse the…

Information Theory · Computer Science 2015-05-21 Darryn Bryant , Charles Colbourn , Daniel Horsley , Padraig Ó Catháin

Due to the zero nontrivial aperiodic correlation of complete complementary code (CCCs), it is used in asynchronous multi carrier code division multiple access (MC-CDMA) communication to provide zero interference performance. However, there…

Information Theory · Computer Science 2021-05-24 Bingsheng Shen , Yang Yang , Zhengchun Zhou

In this paper, we are concerned about optimal two-dimensional optical orthogonal codes with $\lambda$ = 2. Some combinatorial constructions are presented and many infinite families of optimal two-dimensional optical orthogonal codes with…

Combinatorics · Mathematics 2013-12-31 Tao Feng , Yanxun Chang

We introduce two constructions of additive codes over finite fields. Both constructions start with a linear code over a field with $q$ elements and give additive codes over the field with $q^h$ elements whose minimum distance is…

Information Theory · Computer Science 2025-06-05 Simeon Ball , Tabriz Popatia

Complete complementary codes (CCCs) play a vital role not only in wireless communication, particularly in multicarrier systems where achieving an interference-free environment is of paramount importance, but also in the construction of…

Information Theory · Computer Science 2024-03-25 Palash Sarkar , Chunlei Li , Sudhan Majhi , Zilong Liu

It is well known that quantum codes can be constructed by means of classical symplectic dual-containing codes. This paper considers a family of two-generator quasi-cyclic codes and derives sufficient conditions for these codes to be…

Information Theory · Computer Science 2023-01-09 Chaofeng Guan , Ruihu Li , Liangdong Lu , Yu Yao

We show an interesting PBD-closure result for the set of lengths of constant-composition codes whose distance and size meet certain conditions. A consequence of this PBD-closure result is that the size of optimal constant-composition codes…

Information Theory · Computer Science 2007-12-18 Yeow Meng Chee , Alan C. H. Ling , San Ling , Hao Shen

From cosets of binary Hamming codes we construct diameter perfect constant-weight ternary codes with weight $n-1$ (where $n$ is the code length) and distances 3 and 5. The class of distance 5 codes has parameters unknown before. Keywords:…

Combinatorics · Mathematics 2009-08-03 Denis Krotov

Some combinatorial designs, such as Hadamard matrices, have been extensively researched and are familiar to readers across the spectrum of Science and Engineering. They arise in diverse fields such as cryptography, communication theory, and…

Combinatorics · Mathematics 2023-11-08 Ronan Egan