10 problems

Nth-order real quasi-orthogonality conjecture. The permuted matrix satisfies

Second-order real quasi-orthogonality conjecture. The matrix $\mathbf{H}^2_{K/4}$ is real quasi-orthogonal. After permuting its columns according to the index sets…

Real quasi-orthogonality conjecture. The permutation above is real quasi-orthogonal: the $\boldsymbol{p}_{0:N}$-indexed columns and rows of the $N$-by-$N$ GABBA reduced encoded cha…

An orthogonal design $OD(n;s_1,\ldots,s_k)$ is a matrix in variables whose transpose product is $(s_1x_1^2+\cdots+s_kx_k^2)I_n$; in the notation used here, $OD(128;2^3_{(16)})$ den…

A balanced complex orthogonal design (BCOD) with rate $k/p=1/2$ uses $n=2m$ antennas and has decoding delay $p$, with constructions having $p=2^m$. For $m\equiv 0\pmod 4$, Adams et…

COD integral admissibility conjecture. A COD over $\mathbb{C}$ with size $[p,n,k]$ exists if and only if it is admissible for COD over $\mathbb{Z}$, that is, COD without linear com…

Shapiro's conjecture. An OD over the field $\mathbb{C}$ with size $[p,n,k]$ is admissible if and only if the same size is admissible over the ring $\mathbb{Z}$.

For a positive integer $n$, let $u(n)$ denote the decoding delay of the proposed rate-$frac{1}{2}$ scaled complex orthogonal design for $n$ transmit antennas. **Minimal-delay conj…

Let $a$ be such that $a+1$ is not a power of two. Consider square complex orthogonal designs (SCODs) with $2^a$ transmit antennas, rate $\frac{a+1}{2^a}$, and the signaling complex…

Jiang's conjecture. The optimal LD code for i.i.d. channels with binary inputs is the generalized orthogonal design.