Some Optimal and Quasi-Optimal Binary Codes from Cyclic Codes over GF(2m)

Katsumi SAKAKIBARA  Masao KASAHARA  Yoshiharu YUBA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E79-A   No.10   pp.1737-1738
Publication Date: 1996/10/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Information Theory and Coding Theory
optimal binary codes,  binary image of cyclic codes,  Griesmer bound,  concatenated structure,  

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It is shown that five optimal and one quasioptimal binary codes with respect to the Griesmer bound can be obtained from cyclic codes over GF(2fm). An [m(2em - 1), em, 2em-1m] code, a [3(22e - 1), 2e, 3・22e-1] code, a [2(22e - 1), 2, (22e+2 - 4)/3] code, a [3(22e - 1), 2, 22e+1 - 2] code, and a [3(22e - 1), 2(e+1), 3・22e-1 - 2] code are optimal and a [2(22e - 1), 2(e + 1), 22e - 2] code is quasi-optimal.