Self-Dual Codes over R_k and Binary Self-Dual Codes
Keywords:
self-dual codes, codes over R_k, extremal codes, local ringsAbstract
We study self-dual codes over the infinite family of rings R_k, which has been recently introduced to the literature.We prove that for each self-dual code over R_k, k \geq 2, there
exist a corresponding binary self-dual code, a real unimodular
lattice, a complex unimodular lattice, a quaternionic lattice and an
infinite family of self-dual codes. We prove the existence of Type
II codes of all lengths over R_k, for k\geq 3, and we obtain some
extremal binary self-dual codes including the extended binary Golay
code as the Gray images of self-dual codes over R_k for some
suitable k. The binary self-dual codes obtained from R_k all have automorphism groups whose orders are a multiple of 2^k.
Downloads
Published
2013-01-23
Issue
Section
Discrete Mathematics
License
Upon acceptance of an article by the journal, the author(s) accept(s) the transfer of copyright of the article to European Journal of Pure and Applied Mathematics.
European Journal of Pure and Applied Mathematics will be Copyright Holder.
How to Cite
Self-Dual Codes over R_k and Binary Self-Dual Codes. (2013). European Journal of Pure and Applied Mathematics, 6(1), 89-106. https://ejpam.com/index.php/ejpam/article/view/1773