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Two upper bounds on the minimum distance of type-1 quasi-cyclic low-density parity-check (QC LDPC) codes are derived. The necessary condition is given for the minimum code distance of such codes to grow linearly with the code length.

Information Theory · Computer Science 2014-01-10 Alexey Frolov , Pavel Rybin

A new method to construct $q$-ary complementary sequence sets (CSSs) and complete complementary codes (CCCs) of size $N$ is proposed by using desired para-unitary (PU) matrices. The concept of seed PU matrices is introduced and a systematic…

Information Theory · Computer Science 2020-01-15 Zilong Wang , Dongxu Ma , Guang Gong , Erzhong Xue

Z-complementary code set (ZCCS) are well known to be used in multicarrier code-division multiple access (MCCDMA) system to provide a interference free environment. Based on the existing literature, the direct construction of optimal ZCCSs…

Information Theory · Computer Science 2022-04-20 Gobinda Ghosh , Sudhan Majhi , Palash Sarkar , Ashish Kumar Upadhyay

In this work, we study linear codes with the folded Hamming distance, or equivalently, codes with the classical Hamming distance that are linear over a subfield. This includes additive codes. We study MDS codes in this setting and define…

Information Theory · Computer Science 2024-06-21 Umberto Martínez-Peñas , Rubén Rodríguez-Ballesteros

Recently, the theory of quantum error control codes has been extended to subsystem codes over symmetric and asymmetric quantum channels -- qubit-flip and phase-shift errors may have equal or different probabilities. Previous work in…

Quantum Physics · Physics 2008-11-11 Salah A. Aly

The entanglement-assisted stabilizer formalism provides a useful framework for constructing quantum error-correcting codes (QECC), which can transform arbitrary classical linear codes into entanglement-assisted quantum error correcting…

Quantum Physics · Physics 2016-02-09 Jihao Fan , Hanwu Chen , Juan Xu

It is an important task to construct quantum maximum-distance-separable (MDS) codes with good parameters. In the present paper, we provide six new classes of q-ary quantum MDS codes by using generalized Reed-Solomon (GRS) codes and…

Information Theory · Computer Science 2019-12-06 Weijun Fang , Fang-Wei Fu

We introduce a new class of rate one-half binary codes: {\bf complementary information set codes.} A binary linear code of length $2n$ and dimension $n$ is called a complementary information set code (CIS code for short) if it has two…

Information Theory · Computer Science 2016-11-15 Claude Carlet , Philippe Gaborit , Jon-Lark Kim , Patrick Solé

Cyclic codes and their various generalizations, such as quasi-twisted (QT) codes, have a special place in algebraic coding theory. Among other things, many of the best-known or optimal codes have been obtained from these classes. In this…

Information Theory · Computer Science 2017-01-05 Nuh Aydin , Ajdin Halilovic

Z-complementary code set (ZCCS), an extension of perfect complementary codes (CCs), refers to a set of two-dimensional matrices having zero correlation zone properties. ZCCS can be used in various multi-channel systems to support, for…

Information Theory · Computer Science 2019-11-11 Palash Sarkar , Sudhan Majhi , Zilong Liu

We present a unified theoretical and computational framework that bridges mathematical quasiperiodicity with classical crystallographic models. Based on a rigorous cut-and-projection construction, the proposed proximal coincidence point set…

Materials Science · Physics 2026-03-24 Suining Xiong , Wenwen Zou , Pingwen Zhang , Kai Jiang

Weak superimposed codes are combinatorial structures related closely to generalized cover-free families, superimposed codes, and disjunct matrices in that they are only required to satisfy similar but less stringent conditions. This class…

Information Theory · Computer Science 2024-09-17 Yu Tsunoda , Yuichiro Fujiwara

A linear code with parameters $[n, k, n - k + 1]$ is called maximum distance separable (MDS), and one with parameters $[n, k, n - k]$ is called almost MDS (AMDS). A code is near-MDS (NMDS) if both it and its dual are AMDS. NMDS codes…

Combinatorics · Mathematics 2026-04-07 Hengfeng Liu , Chunming Tang , Zhengchun Zhou , Dongchun Han , Hao Chen

In this paper, we construct asymmetric quantum error-correcting codes(AQCs) based on subclasses of Alternant codes. Firstly, We propose a new subclass of Alternant codes which can attain the classical Gilbert-Varshamov bound to construct…

Information Theory · Computer Science 2014-01-17 Jihao Fan , Hanwu Chen

This paper introduces a novel class of code sets, called "symmetrical Z-complementary code sets (SZCCSs)" , whose aperiodic auto- and cross- correlation sums exhibit zero-correlation zones (ZCZs) at both the front-end and tail-end of the…

Information Theory · Computer Science 2022-03-28 Yajing Zhou , Zhengchun Zhou , Zilong Liu , Yang Yang , Ping Yang , Pingzhi Fan

In this note, we present a construction of new nonbinary quantum codes with good parameters. These codes are obtained by applying the Calderbank-Shor-Steane (CSS) construction. In order to do this, we show the existence of (classical)…

Quantum Physics · Physics 2017-05-24 Giuliano G. La Guardia

One of the most important and challenging problems in coding theory is to construct codes with best possible parameters and properties. The class of quasi-cyclic (QC) codes is known to be fertile to produce such codes. Focusing on QC codes…

Information Theory · Computer Science 2021-08-17 Dev Akre , Nuh Aydin , Matthew J. Harrington , Saurav R. Pandey

Linear codes with complementary duals (LCD) have a great deal of significance amongst linear codes. Maximum distance separable (MDS) codes are also an important class of linear codes since they achieve the greatest error correcting and…

Information Theory · Computer Science 2019-09-17 Mehmet E. Koroglu , Mustafa Sarı

In this paper we study a special type of quasi-cyclic (QC) codes called skew QC codes. This set of codes is constructed using a non-commutative ring called the skew polynomial rings $F[x;\theta ]$. After a brief description of the skew…

Information Theory · Computer Science 2008-09-16 Taher Abualrub , Ali Ghrayeb , Nuh Aydin , Irfan Siap

Protocol sequences are used in channel access for the multiple-access collision channel without feedback. A new construction of protocol sequences with a guarantee of worst-case system throughput is proposed. The construction is based on…

Information Theory · Computer Science 2010-04-28 Kenneth W. Shum , Wing Shing Wong