6 problems

Let $\gamma\geq 2$, and let $\mathbb{F}$ be a finite field. A lower triangular Toeplitz superregular matrix is a lower triangular Toeplitz matrix whose relevant minors are all nonz…

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

Let $\gamma\geq 2$ and let $p$ be an odd prime. For a vector $(a_1,a_2,\dots,a_{\gamma-1})\in\mathbb{F}_p^{\gamma-1}$, let $S_\gamma$ be the set associated with this vector in the…

Let $\gamma$ be the order of a lower triangular Toeplitz matrix, and let $\mathbb{F}_{2^{\gamma-2}}$ denote the finite field with $2^{\gamma-2}$ elements. An LT-superregular matrix…

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…

Let $l\geq 5$. A superregular $l\times l$ Toeplitz matrix is a matrix with the superregularity property used in the construction of MDP convolutional codes. Gluesing-Luerssen's con…