Abstract
A [6,3,4] code E/sub 6/ over an Abelian group A/sub 4/ with four elements is presented. E/sub 6/ is cyclic, unlike the [6,3,4] hexacode H/sub 6/ over GF(4). However, E/sub 6/ and H/sub 6/ are isomorphic when the latter is viewed as a group code. Differences and similarities between E/sub 6/ and H/sub 6/ are discussed. A dual code of E/sub 6/ is presented. Some binary codes, among them the [24,12,8] Golay, are derived with the aid of E/sub 6/. A related cyclic [4,2,3] code E/sub 4/* is applied to construct the Nordstrom-Robinson code. E/sub 6/ is the smallest member of a class of [2k,k,4] cyclic and reversible codes over A/sub 4/. Another class of cyclic and reversible codes of length 2l+1; l/spl ges/2 and minimum distance 3 over A/sub 4/ is also presented.
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.
