11 problems

Let $C$ be a doubly even binary code of length $n$, and let $\Lambda_C$ be the inverse image of $C$ under the natural map … Let $\mathbb{Z}[\frac{1}{2}\Lambda_C]$ denote the ring g…

Let $C\subset \mathbb{F}_2^n$ be a maximal doubly even binary code, and let $I=(i_0,i_1,\ldots,i_{n-1})$. Consider the Clifford algebra $\mathbb{C}_n$ and the rational Clifford alg…

Choi et al.'s conjecture. There exists a unique binary optimal $[n,k,d_L(n,k)]$ code $C$ which is even-like and contains ${\bf1}$ if and only if

Let $d(n,k)$ denote the largest minimum distance of a binary linear $[n,k]$ code, and let $d_{so}(n,k)$ denote the largest minimum distance of a binary self-orthogonal $[n,k]$ code…

Let $C$ be a binary quasi group code of length $n=2m>2$, and let $\operatorname{PAut}(C)$ denote its permutation automorphism group. Nonexistence conjecture. There is no binary qua…

A polycyclic code over the binary field $\mathbb{F}_2$ may be self-dual, self-orthogonal, or dual-containing. Binary nonexistence conjecture. There is no self-dual, self-orthogonal…

Parameter and weight-distribution conjecture. The parameters of $\mathcal{C}_f$ should be the same as those of the code in the cited theorem, namely the theorem's parameters for th…

The weight-distribution conjecture. The polynomial $f(x)$ is two-to-one over ${\mathbb F}_{2^n}$, the code $\mathcal{C}_{D(f)}$ has parameters

Let $r$, $s$, and $L$ be nonnegative integers with $L\geqslant 2s+r+1$, and let $C\subseteq {\cal W}_s$ be a minimal $(L,s,r)$ PPRIC code. An MIPPR word is a word associated with…

Keith's conjecture.

Let $q$ be an odd prime power, and let ${\mathbf B}$ and ${\mathbf B}_0$ be the incidence matrices of internal points versus secant lines and external points versus passant lines,…