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.

翻译：加法码可能具有比线性码更优的参数。然而，目前已知的此类案例仍然很少，且这类码的显式构造是一个具有挑战性的问题。本文证明，若最小距离足够大，加法码长度的Griesmer型界总是可以精确达到。这解决了最小距离较大时加法码的最优参数问题，并产生了许多性能优于线性码的加法码无限系列。