On the covering structures of two classes of linear codes from perfect nonlinear functions

Authors:
Chao Li;San Ling;Longjiang Qu
Affiliations:
Department of Mathematics and System Sciences, Science College, National University of Defence Technology, Changsha, China and National Mobile Communications Research Laboratory, Southeast Univers ...;Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore;Department of Mathematics and System Sciences, Science College, National University of Defence Technology, Changsha, China and National Mobile Communications Research Laboratory, Southeast Univers ...
Venue:
IEEE Transactions on Information Theory
Year:
2009

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Abstract

In this paper, the weight distributions of two classes of linear codes based on all known explicit perfect nonlinear functions from Fqm to itself are determined using a unified approach. All the minimal codewords of these codes are characterized according to their weights, which suggests that their covering structures are determined. Finally, all the minimal access sets of the secret sharing schemes based on their dual codes are obtained.