few-weightcodes have been constructed and studied for many years, since their fascinating relations to finite geometries, strongly regular graphs and Boolean functions. Simplex codes are one-weight [q(k-1)/q-1, k ,q(...
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few-weightcodes have been constructed and studied for many years, since their fascinating relations to finite geometries, strongly regular graphs and Boolean functions. Simplex codes are one-weight [q(k-1)/q-1, k ,q(k-1)]q -linear codes and they meet all Griesmer bounds on the generalized Hamming weights of linear codes. All the subcodes with dimension r of a [q(k-1)/q-1, k ,q(k-1)]q -simplex code have the same subcodesupportweight q(k-r) (q(r-1))/q-1 for1 <= r <= k. In this paper, we construct linear codes meeting the Griesmer bound of the r-generalized Hamming weight, such codes do not meet the Griesmer bound of the j-generalized Hamming weight for 1 <= j < r. . Moreover these codes have only fewsubcodesupportweights (few-SSW). The weight distributions and the subcodesupportweight distributions of these distance-optimal codes are determined. Linear codes constructed in this paper are natural generalizations of distance-optimal few-weightcodes.
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