On the inequality $$F(x,D^2u)\ge f(u) +g(u)\, |Du|^q$$ F ( x , D 2 u ) ≥ f ( u ) + g ( u ) | D u | q
نویسندگان
چکیده
منابع مشابه
Cyclic codes of arbitrary length over F q + uF q + u 2 F q + . . . + u k − 1 F
In this paper, we study the structure of cyclic codes of an arbitrary length n over the ring Fq + uFq + uFq + . . . + uFq, where u = 0 and q is a power of prime. Also we study the rank for these codes, and we find their minimal spanning sets. This study is a generalization and extension of the works in references [9] and [12], the dual codes over the ring Fq + uFq + uFq, where u3 = 0 are studie...
متن کامل$(1-2u^k)$-constacyclic codes over $\mathbb{F}_p+u\mathbb{F}_p+u^2\mathbb{F}_+u^{3}\mathbb{F}_{p}+\dots+u^{k}\mathbb{F}_{p}$
Let $\mathbb{F}_p$ be a finite field and $u$ be an indeterminate. This article studies $(1-2u^k)$-constacyclic codes over the ring $\mathcal{R}=\mathbb{F}_p+u\mathbb{F}_p+u^2\mathbb{F}_p+u^{3}\mathbb{F}_{p}+\cdots+u^{k}\mathbb{F}_{p}$ where $u^{k+1}=u$. We illustrate the generator polynomials and investigate the structural properties of these codes via decomposition theorem.
متن کاملOn a class of $(\delta+\alpha u^2)$-constacyclic codes over $\mathbb{F}_{q}[u]/\langle u^4\rangle$
Let Fq be a finite field of cardinality q, R = Fq[u]/〈u 〉 = Fq+uFq+u 2 Fq+u 3 Fq (u = 0) which is a finite chain ring, and n be a positive integer satisfying gcd(q, n) = 1. For any δ, α ∈ F×q , an explicit representation for all distinct (δ + αu)-constacyclic codes over R of length n is given, and the dual code for each of these codes is determined. For the case of q = 2 and δ = 1, all self-dua...
متن کاملOn ( 1 − um ) - Cyclic Codes over F 2 + uF 2 + u 2 F 2 + u 3 F
A new Gray map between codes over F2 +uF2 +uF2 +uF2 + ....+ uF2 and codes over F2 is defined. It is proved that the Gray image of a linear (1− um)-cyclic code over F2 + uF2 + uF2 + uF2 + .... + uF2 of length n is a binary distance invariant quasi-cylic code of index 2m−1 and length 2mn. It is also proved that if n is odd, then every code of length 2mn over F2 which is the Gray image of a linear...
متن کاملON CYCLIC DNA CODES OVER 24 1 F u u
In this paper, we study the construction of cyclic DNA codes by cyclic codes over the finite chain ring 2 4 1 F u u . First, we establish a 1-1 correspondence between DNA pairs and the 16 elements of the ring 2 4 1 F u u . Considering the biology features of DNA codes, we investigate the structure and properties of selfreciprocal complement cyclic codes. Hamming minimum di...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 2015
ISSN: 0025-5831,1432-1807
DOI: 10.1007/s00208-015-1280-2