Trace Representation over Fr of Binary Jacobi Sequences with Period pq

Minglong QI  Shengwu XIONG  Jingling YUAN  Wenbi RAO  Luo ZHONG  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E98-A   No.3   pp.912-917
Publication Date: 2015/03/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E98.A.912
Type of Manuscript: LETTER
Category: Cryptography and Information Security
Keyword: 
Jacobi sequence,  trace representation,  indicator function,  quadratic character,  pqth root of unity,  quaternary generalized cyclotomic sequence,  

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Summary: 
In this letter, we give a trace representation of binary Jacobi sequences with period pq over an extension field of the odd prime field Fr. Our method is based on the use of a pqth root of unity over the extension field, and the representation of the Jacobi sequences by corresponding indicator functions and quadratic characters of two primes p and q.