Abstract
We study a construction method of binary reversible self-dual codes in this paper. Reversible codes have good properties in applications, and it is interesting to note that a class of reversible codes is closely connected to BCH codes and LCD codes. We first characterize binary reversible self-dual codes. Using these characteristics of reversible self-dual codes, we find an explicit method for constructing all the binary reversible self-dual codes up to equivalence. Furthermore, using this construction, we obtain nine optimal reversible self-dual codes of length 70 which are all inequivalent, and these codes are all new with respect to binary self-dual codes; they all have the same parameter [70,35,12] and their automorphism groups have the same order two.
| Original language | English |
|---|---|
| Article number | 101714 |
| Journal | Finite Fields and their Applications |
| Volume | 67 |
| DOIs | |
| State | Published - Oct 2020 |
Bibliographical note
Funding Information:The author is supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (NRF-2017R1D1A1B03028251).The author is supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) grant funded by the Korea government (NRF-2018R1A6A3A01013052) and also by Basic Science Research Program through the National Research Foundation of Korea (NRF) grant funded by the Korea government (NRF-2019R1I1A1A01057755).The author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant No. 2019R1A6A1A11051177) and also by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (NRF-2017R1A2B2004574).
Publisher Copyright:
© 2020 Elsevier Inc.
Keywords
- Automorphism
- Equivalence
- Optimal code
- Reversible code
- Self-dual code