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- W2027167819 abstract "Let 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." @default.
- W2027167819 created "2016-06-24" @default.
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- W2027167819 date "1991-11-01" @default.
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- W2027167819 title "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" @default.
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- W2027167819 doi "https://doi.org/10.1016/0012-365x(91)90214-m" @default.
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