# A problem in asymptotic coding theory?

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

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

• What is a minimum weight code? A code containing a unit vector? – Dirk Jul 12 at 14:21
• 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. – Turbo Jul 12 at 14:22
• Ah, so they only contain a single minimal vector? :) – Dirk Jul 12 at 14:23