2022/04/18 by Vidya Sagar, Sagar, Vidya, Ritumoni Sarma +1
Computer Science · Engineering · #05E45 #94B05 #94B60 #94B65 #Advanced Wireless Communication Techniques #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2204.08417
openalex publication_date 2022/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Certain simplicial complexes are used to construct a subset D of \mathbbF2nm and D, in turn, defines the linear code CD over \mathbbF2n that consists of (v⋅ d)d∈ D for v∈ \mathbbF2nm. 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 CD(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, five infinite families of distance optimal codes are obtained, and sufficient conditions for certain linear codes to be minimal are established.