Designs, Codes and Cryptography

, Volume 86, Issue 4, pp 771–784 | Cite as

The primitive idempotents and weight distributions of irreducible constacyclic codes

  • Fengwei LiEmail author
  • Qin Yue


Let \({\mathbb {F}}_q\) be a finite field with q elements such that \(l^v||(q^t-1)\) and \(\gcd (l,q(q-1))=1\), where lt are primes and v is a positive integer. In this paper, we give all primitive idempotents in a ring \(\mathbb F_q[x]/\langle x^{l^m}-a\rangle \) for \(a\in {\mathbb {F}}_q^*\). Specially for \(t=2\), we give the weight distributions of all irreducible constacyclic codes and their dual codes of length \(l^m\) over \({\mathbb {F}}_q\).


Finite field Primitive idempotent Constacyclic code 

Mathematics Subject Classification

11T71 94B05 



The paper is supported by National Natural Science Foundation of China (No. 11601475) and Foundation of Science and Technology on Information Assurance Laboratory (No. KJ-15-009).


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsZaozhuang UniversityZaozhuangPeople’s Republic of China
  2. 2.State Key Laboratory of CryptologyBeijingPeople’s Republic of China
  3. 3.State Key Laboratory of Information Security, Institute of Information EngineeringChinese Academy of SciencesBeijingPeople’s Republic of China
  4. 4.Department of MathematicsNanjing University of Aeronautics and AstronauticsNanjingPeople’s Republic of China

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