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We investigate a $H$ -invariant linear code $C$ over the finite field $F_{p}$ where $H$ is a group of linear transformations. We show that if $H$ is a noncyclic abelian group and $(| H |, p) = 1$ , then the code $C$ is the sum of the centralizer codes $C_{c} (h)$ where $h$ is a nonidentity element of $H$ . Moreover if $A$ is subgroup of $H$ such that $A ≅ Z_{q} \times Z_{q}$ , $q \neq p$ , then dim $C$ is known when the dimension of $C_{c} (K)$ is known for each subgroup $K \neq 1$ of $A$ . In the last few sections we restrict our scope of investigation to a special class of invariant codes, namely affine...

Extremal Polynomials for Obtaining Bounds for Spherical Codes and Designs.

P. Boyvalenkov (1995)

Discrete & computational geometry

Displaying 1 – 6 of 6

Elementary Albeian p-Extensions of Algebraic Function Fields.

Es gibt keinen optimalen (n + 2,3)-Code einer ungeraden Ordnung n.

Évariste Galois et la planète Mars : introduction à la théorie algébrique du codage

Exact solutions to Waring's problem for finite fields

Exploring invariant linear codes through generators and centralizers

Extremal Polynomials for Obtaining Bounds for Spherical Codes and Designs.

Currently displaying 1 – 6 of 6