Abstract
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 l, t 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 \({\mathbb {F}}_q\).
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Acknowledgements
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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Communicated by P. Charpin.
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Li, F., Yue, Q. The primitive idempotents and weight distributions of irreducible constacyclic codes. Des. Codes Cryptogr. 86, 771–784 (2018). https://doi.org/10.1007/s10623-017-0356-2
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DOI: https://doi.org/10.1007/s10623-017-0356-2