9 problems

Common-zero conjecture. Any such element has at least $4$ zeros in common with each of the elements $x_1-\alpha$ and $x_2-\beta$. This anticipated common-zero property is used to c…

Permutation-decoding conjecture. The code $C$ has a permutation decoding algorithm of complexity

Let $C$ be a one-point algebraic-geometric code associated to the curve … over $GF(p^2)$, with length $n=2p(p-1)+p$, and let $X$ be the corresponding curve over a field $F$. Arrang…

Fixed-alphabet decoding hardness conjecture. Maximum likelihood decoding is NP-hard even for a family of algebraic geometry codes with a fixed alphabet.

Let $q$ be a prime power with $q\geq 3$, and let $\mathcal{X}$ be the maximal hyperelliptic curve over $\mathbb{F}_{q^2}$ given by … Let $u_B\in\mathbb{F}_{q^2}[x]$ be an irreducib…

Zero-bound conjecture. No element of $V$ has more than $48-4=44$ zeros in $\mathcal{B}$. This bound is intended to provide the distance estimate for the constructed locally repaira…

Refined Singleton-bound conjecture. The minimum distance satisfies

Let $X$) be a weighted projective variety with orbifold singularities, and let $C$ be a quantum stabilizer code constructed from self-orthogonal algebraic geometry codes on $X$. Wr…

Random-subcode square conjecture. The probability that