Abstract
We introduce linear cyclic codes over the ring F/sub 2/+uF/sub 2/={0,1,u,u~=u+1}, where u/sup 2/=0 and study them by analogy with the Z/sub 4/ case. We give the structure of these codes on this new alphabet. Self-dual codes of odd length exist as in the case of Z/sub 4/-codes. Unlike the Z/sub 4/ case, here free codes are not interesting. Some nonfree codes give rise to optimal binary linear codes and extremal self-dual codes through a linear Gray map.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
