On codes over $$mathbb {F}_{q}+vmathbb {F}_{q}+v^{2}mathbb {F}_{q}$$ |
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| Authors: | A. Melakhessou K. Guenda T. A. Gulliver M. Shi P. Solé |
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| Affiliation: | 1.Department of Mathematics,University of Batna 2,Batna,Algeria;2.Faculty of Mathematics,USTHB,Bab Ezzouar,Algeria;3.Department of Electrical and Computer Engineering,University of Victoria,Victoria,Canada;4.School of Mathematical Sciences,Anhui University,Hefei,People’s Republic of China;5.Department of Mathematics,Université de Vincennes - Paris 8,Saint-Denis,France |
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| Abstract: | In this paper we investigate linear codes with complementary dual (LCD) codes and formally self-dual codes over the ring (R=mathbb {F}_{q}+vmathbb {F}_{q}+v^{2}mathbb {F}_{q}), where (v^{3}=v), for q odd. We give conditions on the existence of LCD codes and present construction of formally self-dual codes over R. Further, we give bounds on the minimum distance of LCD codes over (mathbb {F}_q) and extend these to codes over R. |
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