(1) Department of Mathematics and System Sciences, Science College, National University of Defense Technology, Changsha, 410073, China (2) National Mobile Communications Research Laboratory, Southeast University, Nanjing, 210096, China (3) Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 637313, Republic of Singapore

A new construction of constant-composition codes based on all known perfect nonlinear functions from F _q m to itself is presented, which provides a kind of unified constructions of constant-composition codes based on all known perfect nonlinear functions from F _q m to itself. It is proved that the new constant-composition codes are optimal with respect to the Luo-Fu-Vinck-Chen bound, when m is an odd positive integer greater than 1. Finally, we point out that two constructions of constant-composition codes, proposed by Ding Cunsheng et al. in 2005, are equivalent to two special types of the new constant-composition codes.

Supported in part by the National Natural Science Foundation of China (Grant Nos. 60573028, 60803156), the Open Research Fund of the National Mobile Communications Research Laboratory of Southeast University (Grant No. W200805) and in part by Singapore Ministry of Education Academic Research Fund (Grant No. T206B2204)