On the covering radius of codes

Author

Graham, R.L. ; Sloane, N. J A

Volume

Issue

fYear

1985

fDate

5/1/1985 12:00:00 AM

Firstpage

385

Lastpage

401

Abstract

The covering radius $R$ of a code is the maximal distance of any vector from the code. This work gives a number of new results concerning $t[n, k]$ , the minimal covering radius of any binary code of length $n$ and dimension $k$ . For example $t[n, 4]$ and $t[n, 5]$ are determined exactly, and reasonably tight bounds on $t[n, k]$ are obtained for any $k$ when $n$ is large. These results are found by using several new constructions for codes with small covering radius. One construction, the amalgamated direct sum, involves a quantity called the norm of a code. Codes with norm $\\leq 2 R + 1$ are called normal, and may be combined efficiently. The paper concludes with a table giving bounds on $t[n, k]$ for $n \\leq 64$ .

Keywords

Linear coding; Binary codes; Code standards; Error correction codes; Linear code; Upper bound;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.1985.1057039

Filename

1057039

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=940176