Constructions of optimal LCD codes over large finite fields |
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| Institution: | 1. School of Mathematical Sciences, Anhui University, Hefei, Anhui, 230601, China;2. Department of Mathematics, Royal University of Phnom Penh, 12156 Phnom Penh, Cambodia;3. Key Laboratory of Intelligent Computing Signal Processing, Ministry of Education, Anhui University, No.3 Feixi Road, Hefei, Anhui, 230039, China;4. National Mobile Communications Research Laboratory, Southeast University, China;5. CNRS/LAGA, University of Paris 8, 93 526 Saint-Denis, France |
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| Abstract: | In this paper1, we prove existence of optimal complementary dual codes (LCD codes) over large finite fields. We also give methods to generate orthogonal matrices over finite fields and then apply them to construct LCD codes. Construction methods include random sampling in the orthogonal group, code extension, matrix product codes and projection over a self-dual basis. |
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| Keywords: | Orthogonal matrices Complementary dual codes Matrix product codes Optimal codes |
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