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In recent years, linear complementary pairs (LCP) of codes and linear complementary dual (LCD) codes have gained significant attention due to their applications in coding theory and cryptography. In this work, we construct explicit LCPs of…

Algebraic Geometry · Mathematics 2024-12-31 Alonso S. Castellanos , Adler V. Marques , Luciane Quoos

The non-binary low-density parity-check (NB-LDPC) codes can offer promising performance advantages but suffer from high decoding complexity. To tackle this challenge, in this paper, we consider NB-LDPC codes over finite fields as codes over…

Information Theory · Computer Science 2024-10-30 V. B. Wijekoon , Emanuele Viterbo , Yi Hong

Linear codes with complementary-duals (LCD) are linear codes that intersect with their dual trivially. Multinegacirculant codes of index $2$ that are LCD are characterized algebraically and some good codes are found in this family. Exact…

Information Theory · Computer Science 2017-03-10 Adel Alahmadi , Cem Güneri , Buket Özkaya , Hatoon Shoaib , Patrick Solé

A linear code $C$ with the property that $C \cap C^{\perp} = \{0 \}$ is said to be a linear complementary dual, or LCD, code. In this paper, we consider generalized affine Cartesian codes which are LCD. Generalized affine Cartesian codes…

Information Theory · Computer Science 2024-02-07 Hiram H. López , Felice Manganiello , Gretchen L. Matthews

Cyclic codes are an interesting class of linear codes due to their efficient encoding and decoding algorithms as well as their theoretical importance. BCH codes form a subclass of cyclic codes and are very important in both theory and…

Information Theory · Computer Science 2016-08-09 Shuxing Li , Cunsheng Ding , Hao Liu

Linear codes with complementary duals (abbreviated LCD) are linear codes whose intersection with their dual is trivial. When they are binary, they play an important role in armoring implementations against side-channel attacks and fault…

Information Theory · Computer Science 2017-03-14 Claude Carlet , Sihem Mesnager , Chunming Tang , Yanfeng Qi

From a given $[n, k]$ code $C$, we give a method for constructing many $[n, k]$ codes $C'$ such that the hull dimensions of $C$ and $C'$ are identical. This method can be applied to constructions of both self-dual codes and linear…

Information Theory · Computer Science 2021-08-31 Keita Ishizuka , Ken Saito

Absolute coset leaders were first proposed by the authors which have advantages in constructing binary LCD BCH codes. As a continue work, in this paper we focus on ternary linear codes. Firstly, we find the largest, second largest, and…

Information Theory · Computer Science 2021-04-12 Xinmei Huang , Qin Yue , Yansheng Wu , Xiaoping Shi

Binary linear codes with good parameters have important applications in secret sharing schemes, authentication codes, association schemes, and consumer electronics and communications. In this paper, we construct several classes of binary…

Information Theory · Computer Science 2016-12-15 Deng Tang , Claude Carlet , Zhengchun Zhou

The aim of this work is to study the structure and properties of the binary LCD codes having an automorphisms of odd prime order and to present a method for their construction.

Information Theory · Computer Science 2021-08-04 Stefka Bouyuklieva , Javier de la Cruz

Cyclic codes have efficient encoding and decoding algorithms over finite fields, so that they have practical applications in communication systems, consumer electronics and data storage systems. The objective of this paper is to give eight…

Information Theory · Computer Science 2022-05-02 Lanqiang Li , Li Liu , Shixin Zhu

In this paper, we introduce a general construction of linear codes with small dimension hull from any non LCD codes. Furthermore, we show that for any linear code $\Co$ over $\F_q$ ($q > 3$) with $dim(Hull(\Co))=h$ there exist an equivalent…

Information Theory · Computer Science 2023-06-02 Maouche Youcef

Due to their efficient encoding and decoding algorithms cyclic codes, a subclass of linear codes, have applications in consumer electronics, data storage systems, and communication systems. In this paper, Dickson polynomials of the first…

Information Theory · Computer Science 2016-11-18 Cunsheng Ding

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

As a generalization of cyclic codes, quasi-cyclic (QC) codes contain many good linear codes. But quasi-cyclic codes studied so far are mainly limited to one generator (1-generator) QC codes. In this correspondence, 2-generator and…

Information Theory · Computer Science 2007-07-16 Eric Zhi Chen

BCH codes form an important subclass of cyclic codes, and are widely used in compact discs, digital audio tapes and other data storage systems to improve data reliability. As far as we know, there are few results on $q$-ary BCH codes of…

Information Theory · Computer Science 2024-01-29 Yuqing Fu , Hongwei Liu

The hull of a linear code over finite fields is the intersection of the code and its dual, and linear codes with small hulls have applications in computational complexity and information protection. Linear codes with the smallest hull are…

Information Theory · Computer Science 2023-06-08 Shitao Li , Minjia Shi , Jon-Lark Kim

LCD BCH codes are an important class of cyclic codes which have efficient encoding and decoding algorithms, but their parameters are difficult to determine. The objective of this paper is to study the LCD BCH codes of length…

Information Theory · Computer Science 2023-06-06 Yanhui Zhang

Non-binary linear block codes (NB-LBCs) are an important class of error-correcting codes that are especially competent in correcting burst errors. They have broad applications in modern communications and storage systems. However, efficient…

Information Theory · Computer Science 2026-01-21 Jingyu Lin , Li Chen , Xiaoqian Ye

A novel adaptive binary decoding algorithm for LDPC codes is proposed, which reduces the decoding complexity while having a comparable or even better performance than corresponding non-adaptive alternatives. In each iteration the variable…

Information Theory · Computer Science 2009-04-24 Ingmar Land , Gottfried Lechner , Lars K. Rasmussen