Title :
On the Covering Structures of Two Classes of Linear Codes From Perfect Nonlinear Functions
Author :
Chao Li ; Longjiang Qu ; San Ling
Author_Institution :
Dept. of Math. & Syst. Sci., Nat. Univ. of Defence Technol., Changsha
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.
Keywords :
linear codes; nonlinear functions; codeword; linear codes; perfect nonlinear function; secret sharing scheme; weight distribution; Chaos; Cryptography; Galois fields; Laboratories; Linear code; Mathematics; Mobile communication; Access structures; covering structures; perfect nonlinear functions; weight distributions;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2008.2008145
