Optimum commutative group codes
نویسندگان
چکیده
A method for finding an optimum n-dimensional commutative group code of a given order M is presented. The approach explores the structure of lattices related to these codes and provides a significant reduction in the number of non-isometric cases to be analyzed. The classical factorization of matrices into Hermite and Smith normal forms and also basis reduction of lattices are used to characterize isometric commutative group codes. Several examples of optimum commutative group codes are also presented.
منابع مشابه
Quasideterminant Characterization of MDS Group Codes over Abelian Groups
A group code defined over a group G is a subset of Gn which forms a group under componentwise group operation. The well known matrix characterization of MDS (Maximum Distance Separable) linear codes over finite fields is generalized to MDS group codes over abelian groups, using the notion of quasideterminants defined for matrices over non-commutative rings.
متن کاملCodes through Monoid Rings and Encoding
Cazaran and Kelarev [2] have given necessary and sufficient conditions for an ideal to be the principal; further they described all finite factor rings Zm[X1, · · · , Xn]/I, where I is an ideal generated by an univariate polynomial, which are commutative principal ideal rings. But in [3], Cazaran and Kelarev characterize the certain finite commutative rings as a principal ideal rings. Though, t...
متن کاملMatrix product codes over finite commutative Frobenius rings
Properties of matrix product codes over finite commutative Frobenius rings are investigated. The minimum distance of matrix product codes constructed with several types of matrices is bounded in different ways. The duals of matrix product codes are also explicitly described in terms of matrix product codes.
متن کاملSelf-dual codes over commutative Frobenius rings
We prove that self-dual codes exist over all finite commutative Frobenius rings, via their decomposition by the Chinese Remainder Theorem into local rings. We construct non-free self-dual codes under some conditions, using self-dual codes over finite fields, and we also construct free self-dual codes by lifting elements from the base finite field. We generalize the building-up construction for ...
متن کامل2-D skew constacyclic codes over R[x, y; ρ, θ]
For a finite field $mathbb{F}_q$, the bivariate skew polynomial ring $mathbb{F}_q[x,y;rho,theta]$ has been used to study codes cite{XH}. In this paper, we give some characterizations of the ring $R[x,y;rho,theta]$, where $R$ is a commutative ring. We investigate 2-D skew $(lambda_1,lambda_2)$-constacyclic codes in the ring $R[x,y;rho,theta]/langle x^l-lambda_1,y^s-lambda_2rangle_{mathit{l}}.$ A...
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:
- Des. Codes Cryptography
دوره 74 شماره
صفحات -
تاریخ انتشار 2015