A class of minimal cyclic codes over finite fields |
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Authors: | Fen Li Xiwang Cao |
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Institution: | 1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;2. State Key Laboratory of Information Security (Institute of Information Engineering, Chinese Academy of Sciences), Beijing 100093, China |
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Abstract: | Let be a finite field of odd order and , where are positive integers, are distinct odd primes and . In this paper, we study the irreducible factorization of over and all primitive idempotents in the ring .Moreover, we obtain the dimensions and the minimum Hamming distances of all irreducible cyclic codes of length over . |
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Keywords: | Irreducible factorization Primitive idempotent Irreducible cyclic code |
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