Shimada and Zhang studied the existence of polarizations on some supersingular $K3$ surfaces by reducing the existence of the polarizations to that of ternary [12,5] codes satisfying certain conditions. In this note, we give a classification of ternary [12,5] codes satisfying the conditions. To do this, ternary [10,5] codes are classified for minimum weights 3 and 4.
"On the classification of certain ternary codes of length 12." Hiroshima Math. J. 46 (1) 87 - 96, March 2016. https://doi.org/10.32917/hmj/1459525932