Binary and Ternary Quasi-perfect Codes with Small Dimensions

Details Binary and Ternary Quasi-perfect Codes with Small Dimensions Binary and Ternary Quasi-perfect Codes with Small Dimensions

2007-12-10

arxiv.org/abs/0712.1465v2

IEEE Transactions on Information Theory, vol. 54, issue 9, pp. 4335-4339, 2008

Mathematics

Combinatorics

4 pages

Scientific paper

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 is. 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.

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