2 problems

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The $2n$ upper-bound conjecture for constant-weight $(1,2,n)$ -LRM Gray codes
An $(1,2,n;2)$ -LRMGC is a constant-weight $(1,2,n)$ -LRM Gray code whose codewords all have weight $2$ . The $(1,2,n;2)$ -LRMGC upper-bound conjecture. Every such code has at most…
Conjectureopencoding-theory flash-memories gray-codesarXiv posted 2 days ago
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The legal-codeword density conjecture for $(1,t,n)$ -LRM schemes
Let $t\geq 3$ , and let $M_t$ denote the number of legal codewords in the $(1,t,n)$ -LRM scheme, where codewords have length $n$ over an alphabet of size $t$ . Thus $M_t\leq t^n$ . Leg…
Conjectureopencoding-theory combinatorics flash-memoriesarXiv posted 2 days ago

The 2n2n2n upper-bound conjecture for constant-weight (1,2,n)(1,2,n)(1,2,n)-LRM Gray codes