Parameterized affine codes

Projective parameterized linear codes

In this paper we estimate the main parameters of some evaluation codes which are known as projective parameterized codes. We find the length of these codes and we give a formula for the dimension in terms of the Hilbert function associated to two ideals, one of them being the vanishing ideal of the projective torus. Also we find an upper bound for the minimum distance and, in some cases, we giv...

Affine cartesian codes

We compute the basic parameters (dimension, length, minimum distance) of affine evaluation codes defined on a cartesian product of finite sets. Given a sequence of positive integers, we construct an evaluation code, over a degenerate torus, with prescribed parameters. As an application of our results, we recover the formulas for the minimum distance of various families of evaluation codes.

Almost Affine Codes

Flags of almost affine codes

We describe a two-party wire-tap channel of type II in the framework of almost affine codes. Its cryptological performance is related to some relative profiles of a pair of almost affine codes. These profiles are analogues of relative generalized Hamming weights in the linear case.

On the Main Parameters of Parameterized Codes

In this paper we will estimate the main parameters of some evaluation codes which are known as parameterized codes. We will find the length of these codes and we will give a formula for the dimension in terms of the Hilbert function associated to the vanishing ideal of the projective torus. Also we will find an upper bound for the minimum distance and, in some cases, we will give some lower bou...