2025/01/01 by Kurz, Sascha
Computer Science · Engineering · #004 #510 #Coding theory and cryptography #Cooperative Communication and Network Coding #Galois geometry #Griesmer bound #additive codes #b-symbol distance #graph theory and CDMA systems #linear codes #symbol-pair distance
paper · doi:10.15495/epub_ubt_00008628
openalex publication_date 2025/01/01 · openalex created_date 2025/11/06 · openalex updated_date 2026/07/15
For linear codes over finite fields the optimal parameters are attained by the so-called Griesmer bound (1960) if the minimum distance is sufficiently large. A corresponding geometric construction was given by Solomon and Stiffler (1965). Here we present an analogous result for addittive codes over finite fields and for linear codes with respect to the b-symbol metric. The latter class was introduced by Cassuto and Blaum in 2011 for the special case b=2 and called pair-symbol codes. Here we also present a geometric description of these codes.