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We establish a complete classification of binary group codes with complementary duals for a finite group and explicitly determine the number of linear complementary dual (LCD) cyclic group codes by using cyclotomic cosets. The dimension and…

Information Theory · Computer Science 2022-01-24 Ankan Shaw , Sanjit Bhowmick , Satya Bagchi

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

Linear complementary dual (LCD) codes and linear complementary pairs (LCP) of codes have been proposed for new applications as countermeasures against side-channel attacks (SCA) and fault injection attacks (FIA) in the context of direct sum…

Information Theory · Computer Science 2023-11-03 Sanjit Bhowmick , Deepak Kumar Dalai , Sihem Mesnager

In this manuscript, we introduce a new class of linear codes, called affine symplectic Grassmann codes, and determine their parameters, automorphism group, minimum distance codewords, dual code and other key features. These linear codes are…

Information Theory · Computer Science 2022-06-14 Fernando Piñero González , Doel Rivera Laboy

Recently, Linear Complementary Dual (LCD) codes have garnered substantial interest within coding theory research due to their diverse applications and favorable attributes. This paper directs its attention to the construction of binary and…

Information Theory · Computer Science 2024-09-13 Yansheng Wu , Jin Ma , Shandong Yang

The hull of a linear code over finite fields is the intersection of the code and its dual, which was introduced by Assmus and Key. In this paper, we develop a method to construct linear codes with trivial hull ( LCD codes) and…

Information Theory · Computer Science 2021-03-22 Liqin Qian , Xiwang Cao , Wei Lu , Patrick Sole

In this paper, we propose new coupled codes constructed by overlapping circular spatially-coupled low-density parity-check (SC-LDPC) codes, which show better asymptotic and finite-length decoding performance compared to the conventional…

Information Theory · Computer Science 2018-03-28 Heeyoul Kwak , Bohwan Jun , Pilwoong Yang , Jong-Seon No , Dong-Joon Shin

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

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

Based on the theoretical neuroscience, G. Cotardo and A. Ravagnavi in \cite{CR} introduced a kind of asymmetric binary codes called combinatorial neural codes (CN codes for short), with a "matched metric" $\delta_{r}$ called asymmetric…

Information Theory · Computer Science 2021-12-16 Aixian Zhang , Xiaoyan Jin , Keqin Feng

We present a new application of multi-orbit cyclic subspace codes to construct large optical orthogonal codes, with the aid of the multiplicative structure of finite fields extensions. This approach is different from earlier approaches…

Information Theory · Computer Science 2024-05-30 Ferruh Ozbudak , Paolo Santonastaso , Ferdinando Zullo

Certain simplicial complexes are used to construct a subset $D$ of $\mathbb{F}_{2^n}^m$ and $D$, in turn, defines the linear code $C_{D}$ over $\mathbb{F}_{2^n}$ that consists of $(v\cdot d)_{d\in D}$ for $v\in \mathbb{F}_{2^n}^m$. Here we…

Information Theory · Computer Science 2022-04-19 Vidya Sagar , Ritumoni Sarma

Locally recoverable (LRC) codes provide a solution to single node failure in distributed storage systems, where it is a very common problem. On the other hand, linear complementary dual (LCD) codes are useful in fault injections attacks on…

Information Theory · Computer Science 2020-11-09 Charul Rajput , Maheshanand Bhaintwal , Ramakrishna Bandi

Polycyclic codes offer a natural generalization of cyclic codes and provide a broader algebraic framework for constructing linear codes with good parameters. In this paper, we study binary polycyclic codes associated with powers of…

Information Theory · Computer Science 2026-05-13 Sujata Bansal , Pramod Kumar Kewat

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

In this article, first we present a method for constructing many Hermitian LCD codes from a given Hermitian LCD code, and then provide several methods which utilize either a given [n, k, d] linear code or a given [n, k, d] Galois LCD code…

Information Theory · Computer Science 2023-10-09 Gyanendra K. Verma , Astha Agrawal , R. K. Sharma

In this paper, we study the complementary dual codes in more general setting (which are called Galois LCD codes) by a uniform method. A necessary and sufficient condition for linear codes to be Galois LCD codes is determined, and…

Information Theory · Computer Science 2017-05-03 Xiusheng Liu , Yun Fan , Hualu Liu

We give a method of constructing self-orthogonal codes from equitable partitions of association schemes. By applying this method we construct self-orthogonal codes from some distance-regular graphs. Some of the obtained codes are optimal.…

Combinatorics · Mathematics 2019-03-06 Dean Crnkovic , Sanja Rukavina , Andrea Svob

In this paper, we construct three binary linear codes $C(SO^{-}(2,q))$, $C(O^{-}(2,q))$, $C(SO^{-}(4,q))$, respectively associated with the orthogonal groups $SO^{-}(2,q)$, $O^{-}(2,q)$, $SO^{-}(4,q)$, with $q$ powers of two. Then we obtain…

Number Theory · Mathematics 2008-08-25 Dae San Kim