Codewords of small weight in the (dual) code of points and k-spaces of PG(n, q)
نویسندگان
چکیده
In this paper, we study the p-ary linear code Ck(n, q), q = p , p prime, h ≥ 1, generated by the incidence matrix of points and k-dimensional spaces in PG(n, q). We note that the condition k ≥ n/2 arises in results on the codewords of Ck(n, q). For k ≥ n/2, we link codewords of Ck(n, q)\ Ck(n, q) ⊥ of weight smaller than 2q to k-blocking sets. We first prove that such a k-blocking set is uniquely reducible to a minimal k-blocking set, and exclude all codewords arising from small linear k-blocking sets. For k < n/2, we present counterexamples to lemmas valid for k ≥ n/2. Next, we study the dual code of Ck(n, q) and present a lower bound on the weight of the codewords, hence extending the results of Sachar [12] to general dimension.
منابع مشابه
The Dual Code of Points and t-Spaces in the Projective Space
The most important results on C⊥ t (n, q), the dual code of points and t-spaces in PG(n, q) are presented. We focus on the minimum distance and on the small weight codewords. In the third section, a recent result about the classification of the small weight codewords in C⊥ n−1(n, q), q even, is given.
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