AntiGriesmer Bounds, Optimal Codes, and Their Subcode Support Weight Distributions

In this paper, we present an antiGriesmer lower bound on the subcode support weights of projective linear codes. This bound is a lower bound on the maximum <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i>-dimensional subcode support weights of projective linear codes. Based on the r-dimensional subcode support weight distributions (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i>-SSWDs)