Trace Representation of Binary Generalized Cyclotomic Sequences with Length pm

Xiaoni DU; Zhixiong CHEN

doi:10.1587/transfun.E94.A.761

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

Online ISSN : 1745-1337
Print ISSN : 0916-8508

Regular Section

Trace Representation of Binary Generalized Cyclotomic Sequences with Length p^m

Xiaoni DU, Zhixiong CHEN

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Keywords: binary sequence, finite field, trace function, generalized cyclotomic sequence, linear complexity, defining pair

JOURNAL RESTRICTED ACCESS

2011 Volume E94.A Issue 2 Pages 761-765

DOI https://doi.org/10.1587/transfun.E94.A.761

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Abstract

Some new generalized cyclotomic sequences defined by C. Ding and T. Helleseth are proven to exhibit a number of good randomness properties. In this paper, we determine the defining pairs of these sequences of length p^m (p prime, m å 2) with order two, then from which we obtain their trace representation. Thus their linear complexity can be derived using Key's method.

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