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The minimum distance of a parameterized code over an even cycle

Eduardo Camps-Moreno, Jorge Neves, Eliseo Sarmiento

Abstract

We compute the minimum distance of the parameterized code of order 1 over an even cycle.

The minimum distance of a parameterized code over an even cycle

Abstract

We compute the minimum distance of the parameterized code of order 1 over an even cycle.
Paper Structure (6 sections, 5 theorems, 43 equations)

This paper contains 6 sections, 5 theorems, 43 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. The set of points
  4. The code
  5. Number of zeros of forms
  6. The result

Key Result

Lemma 2.2

Given $F\in S$, if $f=F(x_1x_2,\dots,x_{2k-1}x_{2k},x_{2k}x_1)\in \mathbb{F}[x_1,\dots,x_n]$, the cardinality of $Z(F)\cap X$ is $\mathbf{z}(f)/(q-1)^2$.

Theorems & Definitions (13)

  • Definition 1.1
  • Definition 1.2
  • Definition 2.1
  • Lemma 2.2
  • Theorem 3.1
  • Proposition 3.2
  • proof
  • Lemma 3.3
  • proof
  • Proposition 3.4
  • ...and 3 more