Notes on lcd codes over frobenius rings

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August undefined, 2024

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... WebFrobenius ring, Section 3 will show its idempotents and the related decom-position of a R -module in RG. Sections 4 & 5 study when a group code is LCP in the case of the base ring being a a non-commutative ﬁnite local ring or a non-commutative ﬁnite Frobenius ring respectively. Finally, in Section 6, we deal with checkable codes in RG. 2.

Galois LCD codes over rings - R Discovery

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. WebLCD 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 grapich t-shirt back groud cropped out

Non-Invertible-Element Constacyclic Codes over Finite PIRs

WebJun 15, 2024 · We define a Gray map φ and obtain many maximum-distance-separable (MDS) and optimal 𝔽_q-linear codes from the Gray images of cyclic codes. Under certain conditions we determine linear complementary dual (LCD) codes of length n when (n,q)≠ 1 and (n,q)= 1, respectively. WebLCD 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 ... 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. … grapichs pack good for fivem

Galois LCD codes over rings - aimsciences.org

Do non-free LCD codes over finite commutative Frobenius rings

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 … WebFeb 1, 2024 · This paper sets a foundation for the study of linear codes over finite rings. The finite Frobenius rings are singled out as the most appropriate for coding theoretic … grapich rukes sims 2 leefishWebMar 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 grapic driver pc download

"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. … " - Notes on lcd codes over frobenius rings

Notes on lcd codes over frobenius rings

Galois LCD Codes Over Fq + uFq + vFq + uvFq - arxiv.org

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. WebNote 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.

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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 … 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 ...

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 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

WebMay 22, 2016 · It is proved that non-free LCD codes do not exist over finite commutative Frobenius local rings, and it is shown that a free constacyclic code over a finite chain ring is an LCD code if and only if it is reversible. 21 PDF ... 1 2 3 ... References SHOWING 1-6 OF 6 REFERENCES Hulls of cyclic and negacyclic codes over finite fields 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. Keyword(s): Frobenius Rings . Lcd Codes Download Full-text Download PDF Package. Related Documents;

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 …

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 … grapid wittenWebIn 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 … grapillard thenezayWebJan 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 ... chitchor castWebJan 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. chitchor 1976WebKeywords: 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 chitchoreWebDec 11, 2013 · Abstract. Properties of matrix product codes over finite commutative Frobenius rings are investigated. The minimum distance of matrix product codes … grapic method for aggregate planningWebKeywords 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 ... chitchor full movie online