Trace Representation over Fr of Binary Jacobi Sequences with Period pq

Minglong QI; Shengwu XIONG; Jingling YUAN; Wenbi RAO; Luo ZHONG

doi:10.1587/transfun.E98.A.912

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

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

Regular Section

Trace Representation over F_r of Binary Jacobi Sequences with Period pq

Minglong QI, Shengwu XIONG, Jingling YUAN, Wenbi RAO, Luo ZHONG

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Keywords: Jacobi sequence, trace representation, indicator function, quadratic character, pqth root of unity, quaternary generalized cyclotomic sequence

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2015 Volume E98.A Issue 3 Pages 912-917

DOI https://doi.org/10.1587/transfun.E98.A.912

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Abstract

In this letter, we give a trace representation of binary Jacobi sequences with period pq over an extension field of the odd prime field F_r. 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.

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