Notes on lcd codes over frobenius rings

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August undefined, 2024

WebJan 30, 2024 · In this paper, we clarify some aspects on LCD codes in the literature. We first prove that a non-free LCD code does not exist over finite commutative Frobenius local rings. We then obtain a necessary and sufficient condition for the existence of LCD code over finite commutative Frobenius rings. WebOct 7, 2024 · Borello M de Cruz J Willems W A note on linear complementary pairs of group codes Discret. ... Fan Y Ling S Liu H Matrix product codes over finite commutative Frobenius rings Des. ... Liu XS Liu H LCD codes over finite chain rings Finite Field Appl. 2015 15 1 19 3333133 10.1016/j.ffa.2015.01.004 1392.94931 Google Scholar Digital Library;

Frobenius Ring - an overview ScienceDirect Topics

WebJan 20, 2024 · 4 Constacyclic LCD codes over finite chain rings Lemma 7. For a polynomial f ( X) of degree r, f^* (X) denotes its reciprocal polynomial and is given by f^* (X)=X^rf... WebOct 6, 2024 · Notes on LCD Codes Over Frobenius Rings Abstract: Let R be a commutative Frobenius local ring. A result that the injective hull of an LCD code C over R. is free of dimension 1(C), where 1(C) is the minimum over the cardinalities of the generating sets … great lakes student loans application

Notes on LCD codes over Frobenius rings Request PDF

WebFeb 28, 2024 · We define the generalized Galois inner product for codes over Frobenius rings, and then present the Galois linear complementary dual (LCD) codes over such rings which generalize the Galois LCD codes over finite fields defined in a recent reference. WebJul 1, 2015 · Under suitable conditions, we provide a necessary and sufficient condition for LCD linear codes over finite chain rings. • We characterize LCD linear codes over finite … WebNov 24, 2024 · 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. flock freight logistics

Finite Frobenius Ring - an overview ScienceDirect Topics

arXiv:1304.6589v2 [cs.IT] 7 Aug 2013

WebMar 31, 2024 · On LCP and checkable group codes over finite non-commutative Frobenius rings DeepAI On LCP and checkable group codes over finite non-commutative Frobenius rings 03/31/2024 ∙ by Sanjit Bhowmick, et al. ∙ Universidad de Valladolid ∙ Universidad Del Norte ∙ 0 ∙ share flock freight ltlWebKeywords: Homogeneous weight, ﬁnite Frobenius rings, reﬂexive partitions MSC (2000): 94B05, 94B99, 16L60 1 Introduction The homogeneous weight has been studied extensively in the literature of codes over rings. It has been introduced by Constantinescu and Heise [6] as a generalization of both the Hamming great lakes student loan contact info

"WebLinear codes over a ﬁnite Frobenius ring also have the extension property [16]. Following a strategy of Dinh and L´opez-Permouth [4], the main result of this paper is that ﬁnite Frobenius rings are characterized by the extension property. That is, if the extension property holds for linear codes over a ﬁnite ring R,thenR is a " - Notes on lcd codes over frobenius rings

Notes on lcd codes over frobenius rings

Non-Invertible-Element Constacyclic Codes over Finite PIRs

WebDec 11, 2013 · Abstract. Properties of matrix product codes over finite commutative Frobenius rings are investigated. The minimum distance of matrix product codes … WebOct 7, 2024 · We first prove that non-free LCD codes do not exist over finite commutative Frobenius local rings. We then obtain a necessary and sufficient condition for the existence of LCD codes over a finite ...

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WebIn this paper, we clarify some aspects of LCD codes in the literature. We first prove that non-free LCD codes do not exist over finite commutative Frobenius local rings. We then obtain … WebOct 6, 2024 · In this paper, we clarify some aspects of LCD codes in the literature. We first prove that non-free LCD codes do not exist over finite commutative Frobenius local rings. …

WebWe define a basis of a code over a finite Frobenius ring as a system of vectors that is independent, modular independent, and spanning. As noted in [1, Remark 2], the two properties of independence and modular independence are logically independent. Exercise 5.7 Let , and , . Show that the system is modular independent, but not independent. WebJan 1, 2024 · Article on Galois LCD codes over rings, published in Advances in Mathematics of Communications 0 on 2024-01-01 by Zihui Liu. Read the article Galois LCD codes over rings on R Discovery, your go-to avenue for effective literature search. ... We describe the judging criterions for a generalized Galois LCD code over a Frobenius ring by introducing ...

WebJul 5, 2024 · We give constructions of self-dual codes over any Frobenius ring. We describe connections to unimodular lattices, binary self-dual codes and to designs. We also describe linear complementary dual codes and make a new definition of a broad generalization encompassing both self-dual and linear complementary codes. Download chapter PDF WebNotes on LCD codes over Frobenius rings IEEE Communications Letters . 10.1109/lcomm.2024.3029073 . 2024 . pp. 1-1. Author(s): Zihui Liu . Xin-Wen Wu. …

WebJan 30, 2024 · In Section 3, we discuss LCD codes over finite commutative Frobenius rings. Finally, Section 4 studies the complementary dual constacyclic codes over finite chain …

WebOct 1, 2024 · Existence of non-free LCD codes over R e, q. In [4], the authors proved that there does not exist any non-free LCD codes over a finite commutative local Frobenius ring, or in other words, every LCD code over a commutative local Frobenius ring is free. Also, the authors gave the conditions in case of a non-local ring for a code to be LCD. flock freight platformWebFeb 28, 2024 · The structure of the generalized Galois LCD codes over chain rings can be used to construct Galois LCD codes over finite fields. By using the structure of the … flock freight supportWebNote that a left and right self-injective semi-primary ring is quasi-Frobenius. (4) The problem whether a self-injective cogenerator ring on the left side (left PF-ring) is a right PF-ring was unsolved until the middle of the 1980's (see Azumaya [Az66], Faith [F76]). Dischinger and W. MüUller [DM86] gave a counterexample in 1986 to this problem. great lakes student loan refinancingWebLCD code over a ﬁnite commutative ring were obtained. A linear code C with parameter [n,k,d] over a ﬁnite ﬁeld is said to be ... Remark 2.1. Note that, above inner product is generalization of Euclidean ... It is well known that for a Frobenius ring R and a linear code C over the ring R of length n, the product of cardinality of C and C ... great lakes student loan routing numberWebLCD code does not exist over ﬁnite commutative Frobenius local rings. We then obtain a necessary and sufﬁcient condition for the existence of LCD code over ﬁnite commutative Frobenius rings. We later show that a free constacyclic code over ﬁnite chain ring is LCD if and only if it is reversible, and great lakes student loans billing contactWebJan 30, 2024 · In this paper, we clarify some aspects on LCD codes in the literature. We first prove that a non-free LCD code does not exist over finite commutative Frobenius local … great lakes student loans account numberWebKeywords Frobenius ring · Linear complementary dual code · Constacyclic code · Chain ring ... Recently, in [20], Liu and Liu studied LCD codes over ﬁnite chain rings and provided a necessary and sufﬁcient condition for a free linear code to be an LCD code over a ﬁnite chain ring. They also gave a sufﬁcient condition [20, Theorem 3.5 ... great lakes student loans contact information