Denote $\mathcal T_n$ to be all 'unique minimum weight' $[n,k]$ binary linear codes.

Is there any evidence that this set has cardinality $\omega(\operatorname{poly}(n))$?

  • $\begingroup$ What is a minimum weight code? A code containing a unit vector? $\endgroup$ – Dirk Jul 12 at 14:21
  • $\begingroup$ Hope it is clearer. Yeap of non-zero weight (all linear codes contain zero weight codeword). Note such a code has trivial symmetry if it exists. I am unsure if it exists. $\endgroup$ – Turbo Jul 12 at 14:22
  • $\begingroup$ Ah, so they only contain a single minimal vector? :) $\endgroup$ – Dirk Jul 12 at 14:23

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