Journal of Applied Mathematics and Computing

, Volume 59, Issue 1–2, pp 741–751 | Cite as

Trace representation of Legendre sequences over non-binary fields

  • Chenhuang WuEmail author
  • Chunxiang Xu
Original Research


For distinct odd primes N and p, we view the N-periodic binary Legendre sequence as a p-ary sequence and present its trace representation via trace functions over \({\mathbb {F}}_p\). We use a skill to calculate the Mattson–Solomon polynomials of Legendre sequences and then describe the Mattson–Solomon polynomials by means of trace functions over \({\mathbb {F}}_p\).


Legendre sequence Trace representation Mattson–Solomon polynomial 

Mathematics Subject Classification

94A55 94A60 65C10 



The work was partially supported by the National Natural Science Foundation of China under Grant Nos. 61772292, 61373140, the National Key R&D Program of China No. 2017YFB0802000, the Natural Science Foundation of Fujian Province under Grant No. 2018J01425 and 2016 Development Program for Distinguished Young Scientific Research Talent of Universities in Fujian Province.


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Copyright information

© Korean Society for Computational and Applied Mathematics 2018

Authors and Affiliations

  1. 1.Center for Cyber Security, School of Computer Science and EngineeringUniversity of Electronic Science and Technology of ChinaChengduPeople’s Republic of China
  2. 2.Provincial Key Laboratory of Applied MathematicsPutian UniversityPutianPeople’s Republic of China

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