7 problems

Let $C$ be a polycyclic code with generator polynomial $g(x)$ satisfying … and suppose that $n$ is prime. Prime-length non-dual-containing conjecture. The code $C$ is not dual-cont…

Binary isoduality characterization conjecture. The code $C$ is isodual if and only if

Let $t_1(x)=x^n-ax^i-b$ and $t_2(x)=x^n-a'x^{n-i}-b'$ satisfy … Let $S_1$ be the set of all polycyclic codes of length $n$ over $\mathbb{F}_q$ associated with $t_1(x)$, and let…

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…

Let $C$ be a polycyclic code over $\mathbb{F}_2$ generated by $g(x)$ dividing $x^n-ax^i-b$. Binary polycyclic-code isoduality conjecture. The code $C$ is iso-dual if and only if…

Let $q$ be a prime power and consider the indicated trinomial-associated polycyclic codes. Iso-dual construction conjecture. The following codes are isodual: - If $q$ is a power of…

Let $t_1(x)=x^n-ax^i-b$ and $t_2(x)=x^n-a'x^{n-i}-b'$ be polynomials in $\bbF_q[x]$ with equal order, and let $C_1$ and $C_2$ denote the sets of length-$n$ polycyclic codes over…