Differential uniformity and constacyclic code from some power mapping

Συγγραφείς: Cui, Yuehui^Aff1, Luo, Jinquan^{Aff1, IDs10623025016624_cor1}

Πηγή: Designs, Codes and Cryptography: An International Journal. 93(9):3671-3687

A tight upper bound on the number of non-zero weights of a constacyclic code

Συγγραφείς: Zhang, Hanglong ^a, Cao, Xiwang ^{a, b, ⁎}

Πηγή: In Finite Fields and Their Applications January 2024 93

Torsion codes of a α-constacyclic code over [formula omitted]

Συγγραφείς: Hesari, Roghaye Mohammadi, Samei, Karim ^⁎

Πηγή: In Discrete Mathematics June 2024 347(6)

The Arithmetic Singleton Bound on the Hamming Distances of Simple-rooted Constacyclic Codes over Finite Fields

Additional Titles: This paper establishes a novel upper bound-termed the arithmetic Singleton bound-on the Hamming distance of any simple-root constacyclic code over a finite field. The key technical ingredient is the notion of multiple equal-difference (MED) representations of the defining set of a simple-root polynomial, which generalizes the MED representation of a cyclotomic coset. We prove that every MED representation induces an upper bound on the minimum distance; the classical Singleton bound corresponds to the coarsest representation, while the strongest among these bounds is defined as the arithmetic Singleton bound. It is shown that the arithmetic Singleton bound is always at least as tight as the Singleton bound, and a precise criterion for it to be strictly tighter is obtained. For irreducible constacyclic codes, the bound is given explicitly by $ω+1$, where $ω$ is a constant closely related to the order of $q$ modulo the radical of the polynomial order. This work provides the first systematic translation of arithmetic structure-via MED representations-into restrictive constraints on the minimum distance, revealing that the Singleton bound may be unattainable not because of linear limitations, but due to underlying algebraic obstructions.

Συγγραφείς: Zhu, Li, Wu, Hongfeng

Όροι ευρετηρίου: Information Theory, text

Σύνδεσμος: http://arxiv.org/abs/2602.11788

A tight upper bound on the number of non-zero weights of a constacyclic code

Συγγραφείς: Zhang, Hanglong, Cao, Xiwang

Θεματικοί όροι: Computer Science - Information Theory

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2305.06505

The dual code of any [formula omitted]-constacyclic code over [formula omitted] of oddly even length

Συγγραφείς: Gao, Yun ^⁎, Fu, Fang-Wei

Πηγή: In Discrete Mathematics August 2019 342(8):2179-2191

The dual of a constacyclic code, self dual, reversible constacyclic codes and constacyclic codes with complementary duals over finite local Frobenius non-chain rings with nilpotency index 3

Συγγραφείς: Castillo-Guillén, C.A. ^{a, ⁎}, Rentería-Márquez, C. ^b, Sarmiento-Rosales, E. ^b, Tapia-Recillas, H. ^c, Villarreal, R.H. ^d

Πηγή: In Discrete Mathematics August 2019 342(8):2283-2296

Constacyclic Codes With Best-Known Parameters

Συγγραφείς: Chen, Z., Sha, M.

Πηγή: IEEE Transactions on Information Theory IEEE Trans. Inform. Theory Information Theory, IEEE Transactions on. 72(7):4837-4849 Jul, 2026

Galois hulls of constacyclic codes over affine algebra rings

Additional Titles: Let $\mathcal A$ the affine algebra given by the ring $\mathbb{F}_q[X_1,X_2,\ldots,X_\ell]/ I$, where $I$ is the ideal $\langle t_1(X_1), t_2(X_2), \ldots, t_\ell(X_\ell) \rangle$ with each $t_i(X_i)$, $1\leq i\leq \ell$, being a square-free polynomial over $\mathbb{F}_q$. This paper studies the $k$-Galois hulls of $λ$-constacyclic codes over $\mathcal A$ regarding their idempotent generators. For this, first, we define the $k$-Galois inner product over $\mathcal A$ and find the form of the generators of the $k$-Galois dual and the $k$-Galois hull of a $λ$-constacyclic code over $\mathcal A$. Then, we derive a formula for the $k$-Galois hull dimension of a $λ$-constacyclic code. Further, we provide a condition for a $λ$-constacyclic code to be $k$-Galois LCD. Finally, we give some examples of the use of these codes in constructing entanglement-assisted quantum error-correcting codes.

Συγγραφείς: Debnath, Indibar, Islam, Habibul, Martínez-Moro, Edgar, Prakash, Om

Όροι ευρετηρίου: Information Theory, 94B05, 94B15, 94B60, text

Σύνδεσμος: http://arxiv.org/abs/2412.08512

Multi-dimensional Constacyclic Codes of Arbitrary Length over Finite Fields

Additional Titles: Multi-dimensional cyclic code is a natural generalization of cyclic code. In an earlier paper we explored two-dimensional constacyclic codes over finite fields. Following the same technique, here we characterize the algebraic structure of multi-dimensional constacyclic codes, in particular three-dimensional $(α,β,γ)$- constacyclic codes of arbitrary length $s\ell k$ and their duals over a finite field $\mathbb{F}_q$, where $α,β,γ$ are non zero elements of $\mathbb{F}_q$. We give necessary and sufficient conditions for a three-dimensional $(α,β,γ)$- constacyclic code to be self-dual.

Συγγραφείς: Bhardwaj, Swati, Raka, Madhu

Όροι ευρετηρίου: Information Theory, 94B15, 94B05, 11T71, text

Σύνδεσμος: http://arxiv.org/abs/2201.01031

Imágenes de Gray de códigos consta-cíclicos sobre anillos de Galois R de índice de nilpotencia 3.

Additional Titles: We will state necessary and sufficient conditions for the imageunder the Gray map of aR-constacyclic code to beFpm-quasi-cyclic code.We study the Witt vectors to get a way to operate theμ-reduction ofp-adic components of the elements of the Galois rings of nilpotency index 3, R=GR(p3,m). We analyze Galois rings, its mostly relevant properties, andwe focus in thep-adic representation of their elements. Later on, we examineconstruction of the Witt vectors rings and its operations, in particular, we getexplicit expressions for operations of addition and product of the elements inthe truncated Witt vectors ring of length3,W3(Fpm). Finally, we will usethese operations and an isomorphism betweenGR(p3,m)andW3(Fpm)toget a way to operate theμ-reductions described above.

Συγγραφείς: García Ramírez, Angel, López Andrade, Carlos, Villa Hernández, David

Πηγή: Integración: Temas de matemáticas, ISSN 0120-419X, Vol. 39, Nº. 1, 2021, pags. 57-78

Όροι ευρετηρίου: Anillo de vectores de Witt, anillos de Galois, represen-taciónp-ádica, códigos consta-cíclicos, códigos cuasi-cíclicos, Witt’s vectors ring, Galois rings, p-adic representation, consta-cyclic codes, quasi-cyclic codes, text (article)

Σύνδεσμος: https://dialnet.unirioja.es/servlet/oaiart?codigo=8648918

Ranks of repeated-root constacyclic code

Συγγραφείς: Li, Hongju, Ding, Jian, Tang, Yongsheng

Πηγή: Wuhan University Journal of Natural Sciences. 21:453-460

Θεματικοί όροι: constacyclic codes, minimal spanning set, rank, 0202 electrical engineering, electronic engineering, information engineering, 02 engineering and technology, Cyclic codes

Περιγραφή αρχείου: application/xml

Infinite families of constacyclic codes supporting 3-designs

Συγγραφείς: Hu, Hongsheng^Aff1, Li, Nian^Aff2, Wu, Yanan^{Aff3, Aff4, IDs10623026019418_cor1}, Zeng, Xiangyong^Aff1

Πηγή: Designs, Codes and Cryptography: An International Journal. 94(9)

Non-Invertible-Element Constacyclic Codes over Finite PIRs

Additional Titles: In this paper we introduce the notion of $λ$-constacyclic codes over finite rings $R$ for arbitary element $λ$ of $R$. We study the non-invertible-element constacyclic codes (NIE-constacyclic codes) over finite principal ideal rings (PIRs). We determine the algebraic structures of all NIE-constacyclic codes over finite chain rings, give the unique form of the sets of the defining polynomials and obtain their minimum Hamming distances. A general form of the duals of NIE-constacyclic codes over finite chain rings is also provided. In particular, we give a necessary and sufficient condition for the dual of an NIE-constacyclic code to be an NIE-constacyclic code. Using the Chinese Remainder Theorem, we study the NIE-constacyclic codes over finite PIRs. Furthermore, we construct some optimal NIE-constacyclic codes over finite PIRs in the sense that they achieve the maximum possible minimum Hamming distances for some given lengths and cardinalities.

Συγγραφείς: Liu, Hongwei, Liu, Jingge

Όροι ευρετηρίου: Information Theory, 94B05, 94B60, 94B65, text

Σύνδεσμος: http://arxiv.org/abs/2011.12049

Construction of repeated-root constacyclic code of length 8 p s over $F_{p^m } $

Συγγραφείς: Xiaoyan Zhang, Qili Mao

Πηγή: Wuhan University Journal of Natural Sciences. 20:1-7

Θεματικοί όροι: 0202 electrical engineering, electronic engineering, information engineering, 0102 computer and information sciences, 02 engineering and technology, 01 natural sciences, 3. Good health

On the b-Symbol Distances of Matrix Product Codes, Constacyclic Codes, and Reed-Muller Codes

Συγγραφείς: Pan, X., Ling, S., Liu, H., Chen, B.

Πηγή: IEEE Transactions on Information Theory IEEE Trans. Inform. Theory Information Theory, IEEE Transactions on. 71(1):287-296 Jan, 2025

Two Classes of Constacyclic Codes With a Square-Root-Like Lower Bound

Συγγραφείς: Chen, T., Sun, Z., Xie, C., Chen, H., Ding, C.

Πηγή: IEEE Transactions on Information Theory IEEE Trans. Inform. Theory Information Theory, IEEE Transactions on. 70(12):8734-8745 Dec, 2024

Gray functions and self-orthogonal codes on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$GF(2^d)[X,Y,Z]/\langle X^2, Y^2, YZ, XZ, Z^2-XY\rangle $$\end{document}

Συγγραφείς: Álvarez-García, Cain^{Aff1, IDs0020002600733w_cor1}, Castillo-Guillén, Carlos Alberto^Aff2, Badaoui, Mohamed^Aff2, Robles-García, Jaime^Aff2

Πηγή: Applicable Algebra in Engineering, Communication and Computing. :1-28

Skew constacyclic codes of length \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p^s$$\end{document} over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {F}_{p^m}+u\mathbb {F}_{p^m}+u^2\mathbb {F}_{p^m}$$\end{document}

Συγγραφείς: Hesari, Roghaye Mohammadi^Aff1, Samei, Karim^{Aff1, IDs4099502501896w_cor1}

Πηγή: Iranian Journal of Science. 50(1):265-278

Galois hulls of constacyclic codes over affine algebra rings

Συγγραφείς: Debnath, Indibar ^a, Islam, Habibul ^b, Martínez-Moro, E. ^c, Prakash, Om ^{a, ⁎}

Πηγή: In Discrete Mathematics August 2025