On Constant-Weight Multi-Valued Sequences from Cyclic Difference Sets

Takayasu KAIDA  Junru ZHENG  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E96-A   No.1   pp.171-176
Publication Date: 2013/01/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E96.A.171
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
Category: Foundations
constant-weight sequence,  multi-valued sequence,  cyclic difference set,  value distribution,  linear complexity,  correlation property,  

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We proposed a method for constructing constant-weight and multi-valued sequences from the cyclic difference sets by generalization of the method in binary case proposed by N. Li, X. Zeng and L. Hu in 2008. In this paper we give some properties about sets of such sequences and it is shown that a set of non-constant-weight sequences over Z4 with length 13 from the (13,4,1)-cyclic difference set, and a set of constant-weight sequences over Z5 with length 21 from the (21,5,1)-cyclic difference set have almost highest linear complexities and good profiles of all sequences' linear complexities. Moreover we investigate the value distribution, the linear complexity and correlation properties of a set of sequences with length 57 over GF(8) from the (57,8,1)-cyclic difference set. It is pointed out that this set also has good value distributions and almost highest linear complexities in similar to previous two sets over Z4 with length 13 and Z5 with length 21.