Author:
Pawlina John,Tohǎneanu Ştefan O.
Abstract
AbstractLet $${{\mathbb {K}}}$$
K
be any field, let $$X\subset {\mathbb P}^{k-1}$$
X
⊂
P
k
-
1
be a set of $$n$$
n
distinct $${{\mathbb {K}}}$$
K
-rational points, and let $$a\ge 1$$
a
≥
1
be an integer. In this paper we find lower bounds for the minimum distance $$d(X)_a$$
d
(
X
)
a
of the evaluation code of order $$a$$
a
associated to $$X$$
X
. The first results use $$\alpha (X)$$
α
(
X
)
, the initial degree of the defining ideal of $$X$$
X
, and the bounds are true for any set $$X$$
X
. In another result we use $$s(X)$$
s
(
X
)
, the minimum socle degree, to find a lower bound for the case when $$X$$
X
is in general linear position. In both situations we improve and generalize known results.
Publisher
Springer Science and Business Media LLC