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Optimality conjecture for linear binary $(n,2)$ codes on the BSC
Linear-code optimality conjecture. For every block length $n$ , a best linear $(n,2)$ code is optimal among all binary $(n,2)$ codes in terms of ML decoding performance.
Conjectureopenbinary-symmetric-channels coding-theory finite-length-codesarXiv posted 2 days ago

Optimality conjecture for linear binary (n,2)(n,2)(n,2) codes on the BSC