Galois LCD codes over finite fields |
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| Institution: | 1. School of Mathematics and Physics, Hubei Polytechnic University, Huangshi, Hubei 435003, China;2. School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei 430079, China |
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| Abstract: | In this paper, we generalize the linear complementary dual codes (LCD codes for short) to k-Galois LCD codes, and study them by a uniform method. A necessary and sufficient condition for linear codes to be k-Galois LCD codes is obtained, two classes of k-Galois LCD MDS codes are exhibited. Then, necessary and sufficient conditions for λ-constacyclic codes being k-Galois LCD codes are characterized. Some classes of k-Galois LCD λ-constacyclic MDS codes are constructed. Finally, we study Hermitian LCD λ-constacyclic codes, and present a class of Hermitian LCD λ-constacyclic MDS codes. |
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| Keywords: | Constacyclic code MDS code Cyclotomic coset |
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