The primitive idempotents and weight distributions of irreducible constacyclic codes |
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| Authors: | Fengwei Li Qin Yue |
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| Institution: | 1.School of Mathematics and Statistics,Zaozhuang University,Zaozhuang,People’s Republic of China;2.State Key Laboratory of Cryptology,Beijing,People’s Republic of China;3.State Key Laboratory of Information Security, Institute of Information Engineering,Chinese Academy of Sciences,Beijing,People’s Republic of China;4.Department of Mathematics,Nanjing University of Aeronautics and Astronautics,Nanjing,People’s Republic of China |
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| 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 \(\mathbb F_qx]/\langle x^{l^m}-a\rangle \) 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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