583 research outputs found
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
No full textAbstractRecently, 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 q⩾5 and 0⩽α⩽β⩽γ<t where q is a prime power and υl = (ql−1)(q−1) for any integer l⩾0. 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, 0⩽α = 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 k⩾3 and d = 3k−1 −2·3α−3γ
Characterization of {2(q+1)+2,2;t,q}-minihypers in PG(t,q) (t⩾3,qϵ{3,4})
No full textAbstractA set F of f points in a finite projective geometry PG(t,q) is an (f,m; t,q};-minihyper if m (⩾0) is the largest integer such that all hyperplanes in PG(t,q) contain at least m points in F. Hamada and Deza (1988) characterized all {2(q+1)+2,2; t,q}-minihypers for t⩾3, q⩾5. Hamada (1987, 1989) also determined the cases of t=2, q⩾3. In this paper we characterize {2(q+1)+2,2;t,q}-minihypers for t⩾3, qϵ{3,4}. In addition to the previously known constructions, we describe a new {10, 2; 3,3}-minihyper
Review of Learning words from reading: A cognitive model of word-meaning inference; Author: Megumi Hamada; Publisher: Bloomsbury Academic, 2021; ISBN: 978-1-3501-5368-4; Pages: 168
No full textBook Review: Learning words from reading: A cognitive model of word-meaning inference. Author: Megumi Hamada. Publisher: Bloomsbury Academic, 2021. ISBN: 978-1-3501-5368-4. Pages: 16
Characterization of {2(q+1)+2,2;t,q}- min·hypers in PG(t, q) (t⩾3,q⩾5) and its applications to error-correcting codes
No full textAbstractLet F be a set of ƒ points in a finite projective geometry PG(t,q) of t dimensions (cf. Appendix I) where t⩾2,f⩾1 and q is a prime power. If (a)|F ∩ H| ⩾m for any hyperplane H in PG(t,q) and (b) |F ∩ H | = m for some hyperplane H in PG(t,q), then F is said to be an {f,m;t,q}-min·hyper (or an {f,m;t,q}-minihyper) where m ⩾ 0 and |A| denotes the number of elements in the set A.Recently, all {2(q+1)+2,2;2,q}− min·hypers in PG(2, q) have been characterized by Hamada [10, 12] for any prime power q ⩾ 3. The purpose of this paper is to characterize all {2(q+1)+2,2;t,q}−min·hypers in PG(t,q) for any integer t ⩾ 3 and any prime power q ⩾ 5 using the results in Hamada [6−11]. Using those results, all (n,k,d;q)-codes meeting the Griesmer bound (1.1) are characterized for the case k⩾3, d=qk–1 –(2 + 2q) and q⩾5. Those results are a generalization of the results (due to Tamari) which have been published in Discrete Mathematics 49 (1984) 179–191
A characterization of {2vα+1 + 2vβ+1, 2vα + 2vβ; t, q}- minihypers in PG(t, q) (t ⩾ 2, q ⩾ 5 and 0 ⩽ α < β < t) and its applications to error-correcting codes
No full textAbstractLet F be a set of f points in a finite projective geometry PG(t, q) of t dimensions where t ⩾ 2, f ⩾ 1 and q is a prime power. If (a) |F ∩ H| ⩾ m for any hyperplane H in PG(t, q) and (b) |F ∩ H| = m for some hyperplane H in PG(t, q), then F is said to be an {f, m; t, q}-minihyper where m ⩾ 0 and |A| denotes the number of points in the set A.Recently, all {2(q + 1) + 2, 2; 2, q}-minihypers in PG(2, q) have been characterized by Hamada [5−6] for any prime power q ⩾ 3 and all {2(q + 1) + 2, 2; t, q}-minihypers in PG(t, q) have been characterized by Hamada and Deza [9] for any integer t ⩾ 3 and any prime power q ⩾ 5. The purpose of this paper is to extend the above results, i.e., to characterize all {2vα+1 + 2vβ+1, 2vα + 2vβ; t, q}-minihypers in PG(t, q) for any integers α and β such that 0 ⩽ α < β < t where t ⩾ 2, q ⩾ 5 and vl = (ql − 1)(q − 1) for any integer l ⩾ 0. Using those results, all (n, k, d; q)-codes meeting the Griesmer bound are characterized for the case k ⩾ 3, q ⩾ 5 and d = qk−1 − (2qα + 2qβ). Note that v0 = 0, vl = 1 and v2 = q + 1
A Characterization of Some Minihypers in a Finite Projective Geometry PG(t, 4)
No full textRecently, Hamada and Deza [8] gave a complete characterization of all {vα + 1 + vβ + 1 + vγ + 1, vα + vβ + vγ; t, q}-minihypers for any integers α, β, γ, t and any prime power q such that q ⩾ 5 and either 0 ⩽ α = β < γ < t or 0 ⩽ α < β = γ < t where vl = (ql− 1)/(q − 1) for any integer l ⩾ 0. The purpose of this paper is to characterize all {vα + 1 + vβ + 1 + vγ + 1, vα + vβ + vγ; t, q}-minihypers for any integers t, q, α, β and γ such that q = 4 and either (a) 0 ⩽ α < β = γ < t or (b) 0 ⩽ α = β < γ < t and γ ≠ α + 1. Using those results, all (n, k, d ; 4)-codes meeting the Griesmer bound are characterized for the case k ⩾ 3 and d = 4k−1 − 4α − 4β − 4γ
ユウゲン キカ ニオケル テン ト D-FLATS カラ ナル INCIDENCE MATRIX ノ RANK ト MAJORITY DECODABLE CODE ニツイテ ジョウホウ リロン ジッケン ケイカクホウ ニオケル クミアワセ スウガク ノ ショモンダイ ケンキュウカイ ホウコクシュウ
No full textMOUFANG LOOP カラ ツクラレル AFFINE TRIPLE SYSTEM ノ キカガクテキ コウゾウ ト P-RANK ニツイテ ハイチ ノ クミアワセテキ コウゾウ
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