Optimal Additive and Linear b-Symbol Codes for Large Distances

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Kurz, Sascha:
Optimal Additive and Linear b-Symbol Codes for Large Distances.
Bayreuth , 2025 . - 3 S. - (Oberwolfach Reports ; 41/2025 )
DOI: https://doi.org/10.15495/EPub_UBT_00008628

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Abstract

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.