Anticodes in the sum-rank metric
Eimear Byrne, Heide Gluesing-Luerssen, Alberto Ravagnani · Linear Algebra and its Applications · 2022
We study the structure of anticodes in the sum-rank metric for arbitrary fields and matrix blocks of arbitrary sizes. Our main result is a complete classification of optimal linear anticodes. We also compare the cardinality of the ball in the sum-rank metric with that of an optimal linear anticode, showing that the latter is strictly larger over sufficiently large finite fields. Finally, we give examples of parameters for which the largest anticode is neither a ball nor a linear anticode.