Self-dual Permutation Codes of Finite Groups in Semisimple Case
نویسندگان
چکیده
The existence and construction of self-dual codes in a permutation module of a finite group for the semisimple case are described from two aspects, one is from the point of view of the composition factors which are self-dual modules, the other one is from the point of view of the Galois group of the coefficient field.
منابع مشابه
On the existence of self-dual permutation codes of finite groups
The existence and construction of self-dual codes in a permutation module of a finite group for the semisimple case are described from two aspects, one is from the point of view of the composition factors which are self-dual modules, the other one is from the point of view of the Galois group of the coefficient field.
متن کاملA mass formula for self-dual permutation codes
For a module V over a finite semisimple algebra A we give the total number of self-dual codes in V . This enables us to obtain a mass formula for self-dual codes in permutation representations of finite groups over finite fields of coprime characteristic.
متن کاملMultivariable codes over finite chain rings: semisimple codes
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 o...
متن کاملTrellis Structure and Higher Weights of Extremal Self-Dual Codes
A method for demonstrating and enumerating uniformly efficient (permutation-optimal) trellis decoders for self-dual codes of high minimum distance is developed. Such decoders and corresponding permutations are known for relatively few codes. The task of finding such permutations is shown to be substantially simplifiable in the case of self-dual codes in general, and for self-dual codes of suffi...
متن کاملOn the permutation groups of cyclic codes
We classify the permutation groups of cyclic codes over a finite field. As a special case, we find the permutation groups of non-primitive BCH codes of prime length. In addition, the Sylow p-subgroup of the permutation group is given for many cyclic codes of length p. Several examples are given to illustrate the results.
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/1210.1904 شماره
صفحات -
تاریخ انتشار 2012