## Upper bounds on Weight Hierarchies of Extremal Non-Chain Codes

#### Reports in Informatics No. 171, May 1999, Department of
Informatics, University of Bergen, Norway.

#### Abstract

The weight hierarchy of a linear $[n,k;q]$ code \code\ over \GF\ is
the sequence $(d_1,d_2,\ldots,d_k)$ where $d_r$ is the smallest
support size of an $r$-dimensional subcode of \code. The difference
sequence \DS\ is defined by $\delta_i=d_{k-i}-d_{k-i-1}$. An
$[n,k;q]$ code is extremal non-chain if for any $r$ and $s$, where
$1\le r~~We give upper bounds on difference sequences of such codes, give some
general results about codes meeting these bounds with equality, and
finally construct five-dimensional codes meeting the bounds with
equality.
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