Name
Abstract | ||
|---|---|---|
AbstractWe consider the problem of securing data using linear and nonlinearcodes over the binary numbers. We start by developing aconservation law for codes. Then we explain why linear codes, whichare easy to understand and implement, are useful when protecting data from rarely occurring random errors. Bya simple argument, we demonstrate that linear codes are not a good wayto secure data against an attacker.Having ruled out linear codes for this purpose, we take up nonlinearcodes. We explain what a finite field is and how data can berepresented by elements of a finite field. We then consider codesthat are nonlinear functions of the data---the elements ofthe finite field. We show that binary quadratic codes suffer from the samedeficiencies as linear codes.Next we consider cubic codes. First, we show that cubic codes do agood job of detecting changes made by an attacker. Then wedemonstrate that certain cubic codes provide a large measure of protectionagainst attackers and some protection against certain relativelycommon random errors. We show that cubic codes are alsoreasonably efficient in a well-defined sense. Finally, we briefly considerother interesting nonlinear codes. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1137/11085606X | Periodicals |
Keywords | Field | DocType |
robust codes,nonlinear codes,finite fields | Hamming code,Online codes,Mathematical optimization,Low-density parity-check code,Block code,Turbo code,Algorithm,Theoretical computer science,Reed–Solomon error correction,Reed–Muller code,Linear code,Mathematics | Journal |
Volume | Issue | ISSN |
55 | 4 | 0036-1445 |
Citations | PageRank | References |
1 | 0.35 | 5 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Shlomo Engelberg | 1 | 32 | 10.67 |
| Osnat Keren | 2 | 106 | 20.19 |