Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

The Second Generalized Covering Radius of Binary Primitive Double-Error-Correcting BCH Codes

Lev Yohananov, Moshe Schwartz

TL;DR

This work completely determine the second covering radius for binary primitive double-error-correcting BCH codes and provides a lower bound on the second covering radius.

Abstract

We completely determine the second covering radius for binary primitive double-error-correcting BCH codes. As part of this process, we provide a lower bound on the second covering radius for binary primitive BCH codes correcting more than two errors.

The Second Generalized Covering Radius of Binary Primitive Double-Error-Correcting BCH Codes

TL;DR

This work completely determine the second covering radius for binary primitive double-error-correcting BCH codes and provides a lower bound on the second covering radius.

Abstract

We completely determine the second covering radius for binary primitive double-error-correcting BCH codes. As part of this process, we provide a lower bound on the second covering radius for binary primitive BCH codes correcting more than two errors.
Paper Structure (5 sections, 8 theorems, 91 equations)

This paper contains 5 sections, 8 theorems, 91 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Upper Bound
  4. Lower Bound
  5. Conclusion

Key Result

Theorem 1

For all $m\geqslant 3$,

Theorems & Definitions (17)

  • Definition 1
  • Definition 2
  • Theorem 1
  • Lemma 1: CocPin06
  • Lemma 2: Ber84
  • Lemma 3
  • proof
  • Lemma 4
  • proof
  • Theorem 2
  • ...and 7 more