Abstract
For group codes over elementary Abelian groups we present definitions of the generator and the parity check matrices, which are matrices over the ring of endomorphism of the group. We also lift the theorem that relates the parity check and the generator matrices of linear codes over finite fields to group codes over elementary Abelian groups. Some new codes that are MDS, self-dual, and cyclic over the Abelian group with four elements are given.
Keywords
Publication details
- DOI
- 10.24200/squjs.vol8iss2pp145-151
- Journal
- Sultan Qaboos University Journal for Science, 8(2), 145
- Publisher
- Sultan Qaboos University
- Open access
- Gold open access
- License
- CC BY 4.0
Cite this article
APA 7
Zain, A. A. (2003). On Group Codes Over Elementary Abelian Groups. Sultan Qaboos University Journal for Science, 8(2), 145. https://doi.org/10.24200/squjs.vol8iss2pp145-151
MLA 9
Zain, Adnan A. "On Group Codes Over Elementary Abelian Groups." Sultan Qaboos University Journal for Science, vol. 8, no. 2, 2003, pp. 145. https://doi.org/10.24200/squjs.vol8iss2pp145-151.
Chicago (author–date)
Zain, Adnan A. 2003. "On Group Codes Over Elementary Abelian Groups." Sultan Qaboos University Journal for Science 8 (2): 145. https://doi.org/10.24200/squjs.vol8iss2pp145-151.
Harvard
Zain, A. A. (2003) 'On Group Codes Over Elementary Abelian Groups', Sultan Qaboos University Journal for Science, 8(2), pp. 145. doi:10.24200/squjs.vol8iss2pp145-151.
Vancouver
Zain AA. On Group Codes Over Elementary Abelian Groups. Sultan Qaboos University Journal for Science. 2003;8(2):145. doi:10.24200/squjs.vol8iss2pp145-151
IEEE
A. A. Zain, "On Group Codes Over Elementary Abelian Groups," Sultan Qaboos University Journal for Science, vol. 8, no. 2, pp. 145, 2003, doi: 10.24200/squjs.vol8iss2pp145-151.