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，提出了满足Griesmer界的无限码族。这些码随后被称为Solomon-Stiffler码，并推动了满足或接近Griesmer界的各类码的构造研究。本文从几何角度给出了仿射及修正仿射Solomon-Stiffler码无限族的构造方法。射影Solomon-Stiffler码是本工作中修正仿射Solomon-Stiffler码的特殊情形。作为本构造的特例，我们构建了多个无限族的$q$元Griesmer码、最优码、几乎最优二重、三重、四重及五重线性码，并确定了这些Griesmer码、最优码或几乎最优码的重量分布。Grassl列表中的许多最优线性码均可重构为（修正）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像构造了多个最优或Griesmer码的无限族；这些Griesmer码或最优码的参数、重量分布与本构造中某些特例码完全相同。我们还指出，相较于IEEE Transactions on Information Theory近期一篇论文所构造的码，更一般的距离最优二元线性码可直接从二元Solomon-Stiffler码的余维一子码中获得。