مرکز منطقه ای اطلاع رساني علوم و فناوري - A new class of codes meeting the Griesmer bound

DocumentCode :

933774

Title :

A new class of codes meeting the Griesmer bound

Author :

Helleseth, Tor ; Van Tilborg, Henk C A

Volume :

Issue :

fYear :

1981

fDate :

9/1/1981 12:00:00 AM

Firstpage :

548

Lastpage :

555

Abstract :

An infinite sequence of $k$ -dimensional binary linear block codes is constructed with parameters $n=2^{k}+2^{k-2}-15,d=2^{k-1}+2^{k-3}-8,k \\geq 7$ . For $k \\geq 8$ these codes are unique, while there are five nonisomorphic codes for $k=7$ . By shortening these codes in an appropriate way, one finds codes meeting the Griesmer bound for $2^{k-1}+2^{k-3}-15 \\leq d \\leq 2^{k-1}+2^{k-3}-8; k \\geq 7$ .