2024/06/13 by Maria Bras-Amorós, Bras-Amorós, Maria, Alonso S. Castellanos +3
Computer Science · Mathematics · #11T71 #14G50 #14Q05 #94B27 #Algebraic Geometry (math.AG) #Coding theory and cryptography #FOS: Computer and information sciences #FOS: Mathematics #Finite Group Theory Research #Information Theory (cs.IT) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2406.08952
openalex publication_date 2024/06/13 · openalex created_date 2024/06/15 · openalex updated_date 2026/07/28
A flag C0 \subsetneq C1 ⋯ \subsetneq Cs \subsetneq \mathbb Fqn of linear codes is said to be self-orthogonal if the duals of the codes in the flag satisfy Ci^⊥=Cs-i, and it is said to satisfy the isometry-dual property with respect to an isometry vector \bf x if Ci^⊥=\bf x Cs-i for i=1, …, s. We characterize complete (i.e. s=n) flags with the isometry-dual property by means of the existence of a word with non-zero coordinates in a certain linear subspace of \mathbb Fqn. For flags of algebraic geometry (AG) codes we prove a so-called translation property of isometry-dual flags and give a construction of complete self-orthogonal flags, providing examples of self-orthogonal flags over some maximal function fields. At the end we characterize the divisors giving the isometry-dual property and the related isometry vectors showing that for each function field there is only a finite number of isometry vectors and that they are related by cyclic repetitions.