Notes on lcd codes over frobenius 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. WebDec 11, 2013 · with the original linear code, holds for linear codes over finite F rob enius rings. A special class of finite F robenius rings consists o f the finite chain rings, and codes over...

Complementary Dual Subfield Linear Codes Over Finite Fields

Weblinear ℓ-intersection pair of codes over a finite chain ring is observed as a generalization of LCD and LCP codes over a finite chain ring. LCD codes have been first introduced by … 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 how much mg of cholesterol per day https://allcroftgroupllc.com

-INTERSECTION PAIR OF CODES OVER A FINITE …

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; 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. WebKeywords: 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 how do i make my computer hibernate

Do non-free LCD codes over finite commutative Frobenius …

Category:Do non-free LCD codes over finite commutative Frobenius …

Tags:Notes on lcd codes over frobenius rings

Notes on lcd codes over frobenius rings

Cyclic codes over a non-chain ring R_e,q and their application to LCD …

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 … 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 ...

Notes on lcd codes over frobenius rings

Did you know?

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. 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 …

WebKeywords 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 ... 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

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.

WebFeb 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 … how much mg of gabapentin is overdoseWebJan 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 … how much mg of potassium in bananaWebJan 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 … how do i make my cursor biggerWebWe 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 … how do i make my cricut mat sticky againWebJan 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. how much mg of thc is safeWebDec 11, 2013 · Abstract. Properties of matrix product codes over finite commutative Frobenius rings are investigated. The minimum distance of matrix product codes … how do i make my cursor bolderWebLCD 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 ... how do i make my cursor