A bound on the minimum distance of generalized quasi-twisted codes |
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| Institution: | 1. Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Krijgslaan 281, Building S8, 9000 Gent, Flanders, Belgium;2. Department of Mathematics and Data Science, University of Brussels (VUB), Pleinlaan 2, Building G, 1050 Elsene, Brussels, Belgium;3. Department of Mathematics, University of Rijeka, Radmile Matejčić 2, 51000 Rijeka, Croatia;1. Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan 430062, China;2. Wuhan Maritime Communication Research Institute, Wuhan 430079, China;1. Department of Mathematics and Computer Science, Perugia University, Perugia 06123, Italy;2. Institute for Information Transmission Problems (Kharkevich Institute), Russian Academy of Sciences, Moscow 127051, Russian Federation;1. Key Laboratory of Intelligent Computing Signal Processing, Ministry of Education, School of Mathematical Sciences, Anhui University, Hefei, Anhui, 230601, China;2. School of Mathematical Sciences, Anhui University, Hefei, 230601, China;3. Department of Mathematics and Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey;4. I2M, Aix Marseille Univ., Centrale Marseille, CNRS, Marseille, France |
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| Abstract: | Generalized quasi-twisted (GQT) codes form a generalization of quasi-twisted (QT) codes and generalized quasi-cyclic (GQC) codes. By the Chinese remainder theorem, the GQT codes can be decomposed into a direct sum of some linear codes over Galois extension fields, which leads to the trace representation of the GQT codes. Using this trace representation, we first prove the minimum distance bound for GQT codes with two constituents. Then we generalize the result to GQT codes with s constituents. Finally, we present some examples to show that the bound is better than the well-known Esmaeili-Yari bound and sharp in many instances. |
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| Keywords: | Generalized quasi-twisted codes Trace representation The minimum distance bound |
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