Multivariable codes over finite chain rings: semisimple codes
نویسنده
چکیده
The structure of multivariate semisimple codes over a finite chain ring R is established using the structure of the residue field R̄. Multivariate codes extend in a natural way the univariate cyclic and negacyclic codes and include some non-trivial codes over R. The structure of the dual codes in the semisimple abelian case is also derived and some conditions on the existence of selfdual codes over R are studied.
منابع مشابه
Codes over affine algebras with a finite commutative chain coefficient ring
We consider codes defined over an affine algebra A = R[X1, . . . , Xr]/ 〈t1(X1), . . . , tr(Xr)〉, where ti(Xi) is a monic univariate polynomial over a finite commutative chain ring R. Namely, we study the A−submodules of A (l ∈ N). These codes generalize both the codes over finite quotients of polynomial rings and the multivariable codes over finite chain rings. Some codes over Frobenius local ...
متن کاملMultivariable codes in principal ideal polynomial quotient rings with applications to additive modular bivariate codes over $\mathbb{F}_4$
In this work, we study the structure of multivariable modular codes over finite chain rings when the ambient space is a principal ideal ring. We also provide some applications to additive modular codes over the finite field $\mathbb{F}_4$.
متن کاملConstacyclic Codes over Group Ring (Zq[v])/G
Recently, codes over some special finite rings especially chain rings have been studied. More recently, codes over finite non-chain rings have been also considered. Study on codes over such rings or rings in general is motivated by the existence of some special maps called Gray maps whose images give codes over fields. Quantum error-correcting (QEC) codes play a crucial role in protecting quantum ...
متن کاملMDS codes over finite principal ideal rings
The purpose of this paper is to study codes over finite principal ideal rings. To do this, we begin with codes over finite chain rings as a natural generalization of codes over Galois rings GR(pe, l) (including Zpe). We give sufficient conditions on the existence of MDS codes over finite chain rings and on the existence of self-dual codes over finite chain rings. We also construct MDS self-dual...
متن کاملQuantum Codes from Linear Codes over Finite Chain Rings
In this paper, we provide two methods of constructing quantum codes from linear codes over finite chain rings. The first one is derived from the Calderbank-ShorSteane (CSS) construction applied to self-dual codes over finite chain rings. The second construction is derived from the CSS construction applied to Gray images of the linear codes over finite chain ring Fp2m + uFp2m. The good parameter...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005