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Trace Representation over Fr of Binary Jacobi Sequences with Period pq
Minglong QI Shengwu XIONG Jingling YUAN Wenbi RAO Luo ZHONG
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2015/03/01
Online ISSN: 1745-1337
Type of Manuscript: LETTER
Category: Cryptography and Information Security
Jacobi sequence, trace representation, indicator function, quadratic character, pqth root of unity, quaternary generalized cyclotomic sequence,
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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.