Vortrag
Lengths of divisible codes with restricted column multiplicities
Vortrag von Theresa Körner
Datum: 15.03.23 Zeit: 15.00 - 16.00 Raum:
A linear code C over GF(q) is called Delta-divisible if the Hamming weights wt(c) of all codewords c are divisible by Delta. The study of divisible codes was initiated by Harold Ward.
The possible effective lengths of q^r-divisible codes
have been completely characterized for each prime power q and each nonnegative integer r. An implication of these results are upper bound for partial spreads.
More and more applications of divisible codes emerged in the last years, e.g. upper bounds for so-called subspace codes. Noting that the known characterization result for the possible (effective) lengths of q^r-divisible codes involves quite large point multiplicities on the constructive side, there is quite some need for more refined results taking other parameters like the maximum possible point multiplicities or the dimension. Also the restriction that the exponent r in the divisibility constant Delta = q^r has to be an integer is not always met in the applications. In this talk I present some partial results on the possible effective lengths of divisible codes with extra constraints.
(**This eSeminar will take place over Zoom, using the same meeting details as previous seminars. If you do not have meeting details, please contact zita.fiquelideabreu@math.uzh.ch **)