Yet another variation on minimal linear codes

Minimal linear codes are linear codes such that the support of every codeword does not contain the support of another linearly independent codeword. Such codes have applications in cryptography, e.g. to secret sharing. We consider here quasi-minimal, t-minimal, and t-quasi-minimal linear codes, which are new variations on this notion. Part of this work was done by the first two authors and presented at 4th International Castle Meeting on Coding Theory and Applications Palmela, Portugal, 15-18 September 2014; an extended version with all proofs has been submitted to AMC ([CMR14]).