Notes on lcd codes over frobenius rings
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. 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 …
Notes on lcd codes over frobenius rings
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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; 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 ...
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 …
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. 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. …
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 …
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 … eastern house terre haute indianaWebIn 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 ... eastern house terre hauteWebMay 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 eastern house southwoldWebNote 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. eastern howard athleticsWebJul 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 … eastern housing mirpur 12 gymWebKeywords: 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 cufoonWebWe 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 … eastern house terre haute menu