Negacyclic codes of odd length over the ring $\mathbb{F}_p[u, v]/\langle u^2, v^2, uv-vu\rangle$
نویسنده
چکیده
We discuss the structure of negacyclic codes of odd length over the ring Fp[u, v]/〈u , v, uv − vu〉. We find the unique generating set, the rank and the minimum distance for these negacyclic codes.
منابع مشابه
Cyclic codes over the ring $\mathbb{F}_p[u,v] / \langle u^k,v^2,uv-vu\rangle$
Let p be a prime number. In this paper, we discuss the structures of cyclic codes over the ring F p [u, v]/u k , v 2 , uv − vu. We find a unique set of generators for these codes. We also study the rank and the Hamming distance of these codes.
متن کاملCyclic codes over the ring $\mathbb{F}_p[u, v, w]/\langle u^2, v^2, w^2, uv-vu, vw-wv, uw-wu \rangle$
In this paper, we investigate cyclic codes over the ring Fp[u, v, w]〈u , v, w, uv− vu, vw − wv, uw − wu〉, where p is a prime number. Which is a part of family of Frobenius rings. We find a unique set of generators for these codes and characterize the free cyclic codes. We also study the rank and the Hamming distance of these codes. We also constructs some good p−ary codes as the Gray images of ...
متن کامل$(1-2u^2)$-constacyclic codes over $\mathbb{F}_p+u\mathbb{F}_p+u^2\mathbb{F}_p$
Let $\mathbb{F}_p$ be a finite field and $u$ be an indeterminate. This article studies $(1-2u^2)$-constacyclic codes over the ring $\mathbb{F}_p+u\mathbb{F}_p+u^2\mathbb{F}_p$, where $u^3=u$. We describe generator polynomials of this kind of codes and investigate the structural properties of these codes by a decomposition theorem.
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 کاملDNA Cyclic Codes Over The Ring $ \F_2[u, v]/\langle u^2-1, v^3-v, uv-vu \rangle$
In this paper, we mainly study the some structure of cyclic DNA codes of odd length over the ring R = F2[u, v]/〈u 2 − 1, v3 − v, uv − vu〉 which play an important role in DNA computing. We established a direct link between the element of ring R and 64 codons by introducing a Gray map from R to R1 = F2 + uF2, u 2 = 1 where R1 is the ring of four elements. The reverse constrain and the reverse-com...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1501.07431 شماره
صفحات -
تاریخ انتشار 2015