AI 中文总结
该研究给出广义Griesmer界与antiGriesmer界的三种证明，通过剩余码、缩短子码等论证揭示两界等价性，并将Griesmer码的可除性结果推广到antiGriesmer码。
AI 中文摘要
我们给出广义Griesmer界的三种证明，以及对应的广义antiGriesmer界的证明。第一种证明源于关联连续最小与最大子码支撑重量的不等式。我们还将Tsfasman和Vlăduţ的射影构造表述为剩余码论证，并将Kurz、Landjev和Rousseva的几何证明用缩短子码来表述。此外，重复单纯码中的补集表明这两个界等价。剩余与缩短论证还确定了等式对所得剩余码和缩短子码的推论。最后，补集关系将Griesmer码的已知可除性结果推广到antiGriesmer码。
英文摘要
We present three proofs of the generalized Griesmer bound together with the corresponding proofs of the generalized antiGriesmer bound. The first proof follows from inequalities relating consecutive minimum and maximum subcode support weights. We also write the projective construction of Tsfasman and Vlăduţ as a residual code argument and express the geometric proof of Kurz, Landjev, and Rousseva in terms of shortened subcodes. In addition, complements in repeated simplex codes show that the two bounds are equivalent. The residual and shortening arguments also determine the consequences of equality for the resulting residual codes and shortened subcodes. Finally, the complement relation transfers known divisibility results for Griesmer codes to antiGriesmer codes.
Comments20 pages
