A small minimal blocking set in PG(n, pt), spanning a (t-1)-space, is linear
نویسندگان
چکیده
In this paper, we show that a small minimal blocking set with exponent e in PG(n, pt), p prime, spanning a (t/e − 1)-dimensional space, is an Fpe-linear set, provided that p > 5(t/e)− 11. As a corollary, we get that all small minimal blocking sets in PG(n, pt), p prime, p > 5t−11, spanning a (t−1)-dimensional space, are Fp-linear, hence confirming the linearity conjecture for blocking sets in this particular case.
منابع مشابه
On the Linearity of Higher-Dimensional Blocking Sets
A small minimal k-blocking set B in PG(n, q), q = pt, p prime, is a set of less than 3(qk + 1)/2 points in PG(n, q), such that every (n − k)-dimensional space contains at least one point of B and such that no proper subset of B satisfies this property. The linearity conjecture states that all small minimal k-blocking sets in PG(n, q) are linear over a subfield Fpe of Fq. Apart from a few cases,...
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عنوان ژورنال:
- Des. Codes Cryptography
دوره 68 شماره
صفحات -
تاریخ انتشار 2013