Additive codes attaining the Griesmer bound
For coding theorists, this provides a theoretical guarantee for the existence of optimal additive codes in a previously unknown regime, though the result is asymptotic and does not give explicit constructions.
The authors prove that additive codes can always achieve the Griesmer bound when the minimum distance is sufficiently large, solving the problem of optimal parameters for additive codes in that regime and yielding infinite series of additive codes that outperform linear codes.
Additive codes may have better parameters than linear codes. However, still very few cases are known and the explicit construction of such codes is a challenging problem. Here we show that a Griesmer type bound for the length of additive codes can always be attained with equality if the minimum distance is sufficiently large. This solves the problem for the optimal parameters of additive codes when the minimum distance is large and yields many infinite series of additive codes that outperform linear codes.