5 problems

Existence conjecture. For all $n>k>0$ and for all $\delta\geq 0$ there exists an $(n,k,\delta)$ code over a sufficiently large field which is both strongly MDS and has a maximum di…

Superregular matrix existence conjecture. For every integer $b3\geq 5$, there exists a $b3\times b3$ superregular matrix over

MacWilliams identity conjecture. The matrix

Consider a minimal convolutional code with $m$ memory elements and a degree-$v$ distance-spectrum-optimal CRC code, used together under serial list Viterbi decoding at a fixed SNR.…

Let $cgamma$ be an integer with $cgamma dagger 5$. A matrix is superregular Toeplitz if it is both superregular and Toeplitz. Let $n$, $k$, and $cdelta$ be convolutional-code p…