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doi:10.1016/0012-365X(92)90625-P 
Copyright © 1992 Published by Elsevier Science B.V. All rights reserved.
A characterization of some {2υα+1+υγ+1, 2υα+υγ; k−1, 3}- minihypers and some (n,k, 3k−1 − 2 · 3α − 3γ; 3)-codes (k
3, 0
α<γ<k−1) meeting the Griesmer bound*1
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Noboru Hamada
Tor Helleseth
Department of Mathematics, Osaka Women's University, Sakai, Osaka 590, Japan
Department of Informatics, University of Bergen, Thorm
hlensgt. 55, N-5008 Bergen, Norway
Received 5 January 1990;
Abstract
Recently, Hamada and Deza (1988) and Hamada and Helleseth (in a submitted paper) characterized all {υα+1+υβ+1+υγ+1, υα+υβ+υγ; t, q}-minihypers for any integers t, q, α, β and γ such that q5 and 0αβγ<t where q is a prime power and υl = (ql−1)/(q−1) for any integer l0. The purpose of this paper is to characterized all {υα+1+υβ+1+υγ+1,υα+ υβ+υγ;t,q}-minihypers for any integers t, q, α, β and γ such that (a) q = 3, 0α = β< γ<t and γ≠α+1 or (b) q = 3 and (α, β, γ) = (2, 2, 3). Using those results, all (n,k,d; 3)-codes meeting the Griesmer bound are characterized for the case k3 and d = 3k−1 −2·3α−3γ.
Article Outline
*1 Partially supported by The Scandinavia-Japan Sasakawa Foundation. Partially supported by The Norwegian Research Council for Science and the Humanities.
