Linear complementary dual (LCD) codes and self-orthogonal codes have attracted wide attention in recent years for some practical applications. Hence, in this letter, we use simplicial complexes for construction of an infinite family of binary LCD codes and two infinite families of binary self-orthogonal codes. Moreover, we explicitly determine the weight distributions of these codes. We obtain binary LCD codes which have minimum weights two or three, and we also find some self-orthogonal codes meeting the Griesmer bound. As examples, we also present some (almost) optimal binary self-orthogonal codes and LCD distance optimal codes.
Bibliographical noteFunding Information:
Manuscript received December 30, 2019; revised February 2, 2020 and March 10, 2020; accepted March 16, 2020. Date of publication March 20, 2020; date of current version June 10, 2020. This work was supported in part by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education under Grant 2019R1A6A1A11051177, in part by the National Research Foundation of Korea (NRF) funded by the Korea Government through the Ministry of Education, Science and Technology (MEST) under Grant NRF-2017R1A2B2004574, and in part by the Ewha Womans University Research Grant of 2019. The associate editor coordinating the review of this letter and approving it for publication was M. Baldi. (Corresponding author: Yoonjin Lee.) The authors are with the Department of Mathematics, Ewha Womans University, Seoul 03760, South Korea (e-mail: firstname.lastname@example.org; email@example.com). Digital Object Identifier 10.1109/LCOMM.2020.2982381
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- LCD code
- Simplicial complex
- self-orthogonal code
- weight distribution