Notes on lcd codes over frobenius rings
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; 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 …
Notes on lcd codes over frobenius rings
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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 …
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 ... 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.
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 WebDec 11, 2013 · Abstract. Properties of matrix product codes over finite commutative Frobenius rings are investigated. The minimum distance of matrix product codes …
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. fit school rankingWebDec 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... can i cut a rebonded hairWebFrobenius 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. can i cut back hydrangeas in fallWebJan 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 … can i cut augmentin in halfWebOct 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. can i cut back my orchid plantWebJan 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. can i cut back my fiddle leaf figWebIn this work, we shall be largely concerned with codes over finite fields. However, we shall use codes over rings together with a linear Gray map to construct LCD codes. Hence we shall make the definitions in a general setting. A code C of length n over a ring R is a subset of Rn. All rings in this paper are assumed to be commutative rings ... fit school shooting