Lower bounds for constant weight codes

Author

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

Volume

Issue

fYear

1980

fDate

1/1/1980 12:00:00 AM

Firstpage

Lastpage

Abstract

Let $A(n,2\\delta ,w)$ denote the maximum number of codewords in any binary code of length $n$ , constant weight $w$ , and Hamming distance $2\\delta$ Several lower bounds for $A(n,2\\delta ,w)$ are given. For $w$ and $\\delta$ fixed, $A(n,2\\delta ,w) \\geq n^{W-\\delta +l}/w!$ and $A(n,4,w)\\sim n^{w-l}/w!$ as $n \\rightarrow \\infty$ . In most cases these are better than the "Gilbert bound." Revised tables of $A(n,2 \\delta ,w)$ are given in the range $n \\leq 24$ and $\\delta \\leq 5$ .

Keywords

Coding; Algebra; Entropy; Equations; Frequency; Hamming distance; Information geometry; Information theory; Mechanical variables measurement; Probability distribution; Quantum mechanics;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.1980.1056141

Filename

1056141

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=931147