Notes on lcd codes over frobenius rings
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 ... 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
Notes on lcd codes over frobenius rings
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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... 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.
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 … 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 ...
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 … 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.
WebJul 24, 2024 · Some research work on LCD codes over finite Frobenius rings are also carried out. In 2015, Liu et al. [ 9] studied LCD codes over chain rings, and as the main result, they presented a condition for a free code over chain rings to be an LCD code.
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 … cubby definitionWebNotes 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; east brothersWebJan 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 ... cubby de beerWebOct 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 … east brother light station bed \\u0026 breakfastWebOct 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; cubby file transferWebMay 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 cubby cuddlers women\u0027s shoesWebOct 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. east brothers beer