Anzeige
Erschienen in:
22.12.2022
Octanary linear codes using simplicial complexes
Erschienen in: Cryptography and Communications | Ausgabe 3/2023
EinloggenAktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
Abstract
Certain simplicial complexes are used to construct a subset D of \(\mathbb {F}_{2^{n}}^{m}\) and D, in turn, defines the linear code CD over \(\mathbb {F}_{2^{n}}\) that consists of (v ⋅ d)d∈D for \(v\in \mathbb {F}_{2^{n}}^{m}\). Here we deal with the case n = 3, that is, when CD is an octanary code. We establish a relation between CD and its binary subfield code \(C_{D}^{(2)}\) with the help of a generator matrix. For a given length and dimension, a code is called distance optimal if it has the highest possible distance. With respect to the Griesmer bound, three infinite families of distance optimal codes are obtained, and sufficient conditions for certain linear codes to be minimal are established.