Additive codes attain the Griesmer bound with equality for sufficiently large minimum distance, giving infinite series of optimal codes superior to linear codes.
Optimal additive quaternary codes of dimension $3.5$ and $4$
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abstract
After the optimal parameters of additive quaternary codes of dimension $k\le 3$ have been determined there is some recent activity to settle the next case of dimension $k=3.5$. Here we complete dimension $k=3.5$ and $k=4$. We also solve the problem of the optimal parameters of additive quaternary codes of arbitrary dimension when assuming a sufficiently large minimum distance.
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Additive codes attaining the Griesmer bound
Additive codes attain the Griesmer bound with equality for sufficiently large minimum distance, giving infinite series of optimal codes superior to linear codes.