Binary and Ternary Linear Quasi-Perfect Codes With Small Dimensions

The aim of this work is a systematic investigation of the possible parameters of quasi-perfect (QP) binary and ternary linear codes of small dimensions and preparing a complete classification of all such codes. First, we give a list of infinite families of QP codes which includes all binary, ternary, and quaternary codes known to us. We continue further with a list of sporadic examples of binary and ternary QP codes. Later we present the results of our investigation where binary QP codes of dimensions up to 14 and ternary QP codes of dimensions up to 13 are classified.