Abstract
We investigate the geometry of the support of small weight code- words of dual algebraic geometric codes on smooth complete intersections by applying the powerful tools recently developed by Alain Couvreur. In partic- ular, by restricting ourselves to the case of Hermitian codes, we recover and extend previous results obtained by the second named author joint with Marco
Highlights
In the recent contribution [3], the number of small weight codewords for some families of Hermitian codes is determined
The main ingredient in [3] is a nice geometric characterization of the points in the support of a minimum weight codeword, which turn out to be collinear. We show that such a property is not peculiar to Hermitian codes, but it holds in full generality for dual algebraic geometric codes on any smooth
Let d be the minimum distance of the code C(D, G)∗ and let {Pi1, . . . , Pid } be the points in the support of a minimum weight codeword
Summary
In the recent contribution [3], the number of small weight codewords for some families of Hermitian codes is determined. The main ingredient in [3] is a nice geometric characterization of the points in the support of a minimum weight codeword, which turn out to be collinear (see Corollary 1 and Proposition 2 in [3]).
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