On the geometric constructions of optimal linear codes

摘要

In this paper we generalize the construction of Griesmer codes of Belov type to construct [g(q) (k, d) + t, k, d](q) codes with an integer t > 1, where g(q) (k, d) = Sigma(i=0) (k-1) This leads to the construction of several codes of length g(q)(k, d) + 1, many of which are optimal. We also construct a q-divisible [q(2) + q, 5, q(2) - q](q) code through projective geometry. As a projective dual of the code, we construct optimal codes, giving n(q) (5, d) = g(q) (5, d) + 1 for q(4) - q(3) q(2) <= d <= (q(4) - q(3) - 2q, q >= 3, where nq(k, d) is the minimum length n for which an [n, k, dlq code exists.