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 On LCD codes over finite chain rings Bull. Korean Math. Soc. 2020 Vol. 57, No. 1, 37-50 https://doi.org/10.4134/BKMS.b181173Published online January 31, 2020 Y{\i}lmaz Dur\u{g}un Cukurova University Abstract : Linear complementary dual (LCD) codes are linear codes that intersect with their dual trivially. LCD cyclic codes have been known as reversible cyclic codes that had applications in data storage. Due to a newly discovered application in cryptography, interest in LCD codes has increased again. Although LCD codes over finite fields have been extensively studied so far, little work has been done on LCD codes over chain rings. In this paper, we are interested in structure of LCD codes over chain rings. We show that LCD codes over chain rings are free codes. We provide some necessary and sufficient conditions for an LCD code $C$ over finite chain rings in terms of projections of linear codes. We also showed the existence of asymptotically good LCD codes over finite chain rings. Keywords : LCD codes, projections of linear codes, finite chain rings MSC numbers : Primary 94B05, 11T71 Downloads: Full-text PDF   Full-text HTML