In their fundamental paper published in 1965, G. Solomon and J. J. Stiffler invented infinite families of codes meeting the Griesmer bound. These codes are then called Solomon-Stiffler codes and have motivated various constructions of codes meeting or close the Griesmer bound. In this paper, we give a geometric construction of infinite families of affine and modified affine Solomon-Stiffler codes. Projective Solomon-Stiffler codes are special cases of our modified affine Solomon-Stiffler codes. Several infinite families of $q$-ary Griesmer, optimal, almost optimal two-weight, three-weight, four-weight and five-weight linear codes are constructed as special cases of our construction. Weight distributions of these Griesmer, optimal or almost optimal codes are determined. Many optimal linear codes documented in Grassl's list are re-constructed as (modified) affine Solomon-Stiffler codes. Several infinite families of optimal or Griesmer codes were constructed in two published papers in IEEE Transactions on Information Theory 2017 and 2019, via Gray images of codes over finite rings. Parameters and weight distributions of these Griesmer or optimal codes and very special case codes in our construction are the same. We also indicate that more general distance-optimal binary linear codes than that constructed in a recent paper of IEEE Transactions on Information Theory can be obtained directly from codimension one subcodes in binary Solomon-Stiffler codes.

翻译：1965年，G. Solomon与J. J. Stiffler在其发表的重要论文中，构造了无限多族达到Griesmer界的码。这些码随后被称为Solomon-Stiffler码，并推动了多种达到或接近Griesmer界的码的构造研究。本文中，我们给出了无限多族仿射及修正仿射Solomon-Stiffler码的一种几何构造。射影Solomon-Stiffler码是我们修正仿射Solomon-Stiffler码的特殊情形。作为我们构造的特殊情形，我们构造了多个无限族的$q$元Griesmer码、最优码、几乎最优的二重、三重、四重及五重线性码。这些Griesmer码、最优码或几乎最优码的重量分布被确定。Grassl列表中的许多最优线性码被重新构造为（修正的）仿射Solomon-Stiffler码。在IEEE Transactions on Information Theory 2017与2019年发表的两篇论文中，通过有限环上码的Gray像，构造了多个无限族的最优码或Griesmer码。这些Griesmer码或最优码与我们构造中非常特殊情形码的参数和重量分布是相同的。我们还指出，比近期一篇IEEE Transactions on Information Theory论文中所构造的更一般的距离最优二元线性码，可以直接从二元Solomon-Stiffler码的余维一子码中获得。