Additive codes attaining the Griesmer bound

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.

💡 Research Summary

The paper investigates additive codes—subsets of F_q′^n that are closed under addition—and shows that, when the minimum distance d is sufficiently large, these codes can meet the Griesmer bound with equality. This result extends the classical Solomon–Stiefel construction, which was previously known only for linear codes, to the broader class of additive codes.

The authors begin by formalizing additive codes using the notation