Abstract
The difference g 2− d 2 for a q-ary linear [ n,3, d] code C is studied. Here d 2 is the second generalized Hamming weight, that is, the smallest size of the support of a 2-dimensional subcode of C; and g 2 is the second greedy weight, that is, the smallest size of the support of a 2-dimensional subcode of C which contains a codeword of weight d. For codes of dimension 3, it is shown that the problem is essentially equivalent to finding certain weighting of the points in the projective plane, and weighting which give the maximal value of g 2− d 2 are determined in almost all cases. In particular max( g 2− d 2) is determined in all cases for q⩽9.
Sign-in/Register to access full text options 
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.
