The automorphism group of Generalized Reed-Muller codes

The automorphism group of Generalized Reed-Muller codes

Berger, T. and P. Charpin, The automorphism group of Generalized Reed-Muller codes, Discrete Mathematics 117 (1993) l-17. We prove that the automorphism group of Generalized Reed-Muller codes is the general linear nonhomogeneous group. The Generalized Reed-Muller codes are introduced by Kasami, Lin and Peterson. An extensive study was made by Delsarte, Goethals and Mac-Williams; our result foll...

Generalized Reed-Muller Codes

the possible choices for n and k are rather thinly distributed in the class of all pairs (n, k) with k ~ n--and it is, therefore, often inefficient to make use of such codes in concrete situations (that is, when a desired pair (n, k) is far from any achievable pair). We have succeeded in overcoming this difficulty by generalizing the Reed-Muller codes in such a way that they exist for every pai...

The Generalized Reed-Muller codes in a modular group algebra

First we study some properties of the modular group algebra Fpr [G] where G is the additive group of a Galois ring of characteristic pr and Fpr is the field of p r elements. Secondly a description of the Generalized Reed-Muller codes over Fpr in Fpr [G] is presented.

Generalized State Realizations of Reed-Muller Codes

Automorphism groups of generalized Reed-Solomon codes

We look at AG codes associated to P, re-examining the problem of determining their automorphism groups (originally investigated by Dür in 1987 using combinatorial techniques) using recent methods from algebraic geometry. We classify those finite groups that can arise as the automorphism group of an AG code and give an explicit description of how these groups appear. We give examples of generali...