Abstract
Two isometry groups of combinatorial codes are described: the group of isometries, that is, the group of Hamming isometries from a code to itself and the group of monomial isometries, which is the group of those isometries of a code to itself that extend to monomial maps. Unlike the case of classical linear codes, where these groups are the same, it is shown that for combinatorial codes the groups can be arbitrarily different. In particular, there exist codes with the richest possible group of isometries and the trivial group of monomial isometries. In the paper, the two groups are characterized and codes with predefined isometry groups are constructed.
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.
