On Codes that are Invariant under the Affine Group
نویسنده
چکیده
Let k[V ] be the space of functions from a finite vector space into the algebraically closure of its field of scalars. This paper describes the lattice of subspaces of k[V ] which are invariant under the affine group AGL(V ). The description provides a simple method for finding the submodule generated by any set of functions given as polynomials in the standard coordinates.
منابع مشابه
The Automorphism Groups of BCH Codes and of Some Affine-Invariant Codes Over Extension Fields
Affine-invariant codes are extended cyclic codes of length pm invariant under the affine-group acting on Fpm . This class of codes includes codes of great interest such as extended narrow-sense BCH codes. In recent papers, we classified the automorphism groups of affine-invariant codes [2], [5]. We derive here new results, especially when the alphabet field is an extension field, by expanding o...
متن کاملThe permutation group of affine-invariant extended cyclic codes
The extended cyclic codes of length p” , p a prime, which are invariant under the aff ine-group acting on ffpm, are called affine-invariant codes. Following recent results of Berger, we present the formal expression of the permutat ion group of these codes. Afterwards we give several tools in order to determine effectively the group of a given code or of some infinite class of codes. W e next p...
متن کاملThere Are Not Non-obvious Cyclic Affine-invariant Codes
We show that an affine-invariant code C of length p is not permutation equivalent to a cyclic code except in the obvious cases: m = 1 or C is either {0}, the repetition code or its dual. Affine-invariant codes were firstly introduced by Kasami, Lin and Peterson [KLP2] as a generalization of Reed-Muller codes. This class of codes has received the attention of several authors because of its good ...
متن کاملAbsolutely Sound Testing of Lifted Codes
In this work we present a strong analysis of the testability of a broad, and to date the most interesting known, class of “affine-invariant” codes. Affine-invariant codes are codes whose coordinates are associated with a vector space and are invariant under affine transformations of the coordinate space. Affine-invariant linear codes form a natural abstraction of algebraic properties such as li...
متن کاملSuccinct Representation of Codes with Applications to Testing
Motivated by questions in property testing, we search for linear error-correcting codes that have the “single local orbit” property: i.e., they are specified by a single local constraint and its translations under the symmetry group of the code. We show that the dual of every “sparse” binary code whose coordinates are indexed by elements of F2n for prime n, and whose symmetry group includes the...
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:
- Electr. J. Comb.
دوره 19 شماره
صفحات -
تاریخ انتشار 2012