Given a finite field F_q and a positive integer n, a flag is a sequence of nested F_q-subspaces of a vector space F_q^n and a flag code is a nonempty collection of flags. The projected codes of a flag code are the constant dimension codes containing all the subspaces of prescribed dimensions that form the flags in the flag code. In this paper we address the notion of equivalence for flag codes and explore in which situations such an equivalence can be reduced to the equivalence of the corresponding projected codes. In addition, this study leads to new results concerning the automorphism group of certain families of flag codes, some of them also introduced in this paper.

翻译：给定有限域F_q及正整数n，标志是指向量空间F_q^n中嵌套的F_q-子空间序列，标志码则是标志的非空集合。标志码的投影码是由构成标志码中各标志的指定维数子空间所组成的常维数码。本文探讨标志码的等价概念，并研究在何种情况下这种等价可归结为对应投影码的等价性。此外，本研究还得到了关于某些标志码族（包括本文新引入的族）自同构群的新结果。