Further classifications of codes meeting the Griesmer bound (Corresp.)

Author

Helleseth, Tor

Volume

Issue

fYear

1984

fDate

3/1/1984 12:00:00 AM

Firstpage

395

Lastpage

403

Abstract

For any $(n, k, d)$ binary linear code, the Griesmer bound says that $n \\geq \\sum _{i=0}^{k-1} \\lceil d/2^{i} \\rceil$ , where $\\lceil x \\rceil$ denotes the smallest integer $\\geq x$ . We consider codes meeting the Griesmer bound with equality. These codes have parameters $\\left( s(2^{k} - 1) - \\sum _{i=1}^{p} (2^{u_{i}} - 1), k, s2^{k-1} - \\sum _{i=1}^{p} 2^{u_{i} -1} \\right)$ , where $k > u_{1} > \\cdots > u_{p} \\geq 1$ . We characterize all such codes when $p = 2$ or $u_{i-1}-u_{i} \\geq 2$ for $2 \\leq i \\leq p$ .

Keywords

Linear coding; Block codes; Encoding; Error correction codes; Gas insulated transmission lines; Hamming distance; Information theory; Linear code; Notice of Violation;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.1984.1056867

Filename

1056867

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=938457