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For a $[n,k,n-k+1]_q$ Reed Solomon code is there a polynomial time algorithm to find at least one minimum weight $(n-k+1)$ codeword? I searched in literature and I could not find one and hence I am su …

Good codes (those with positive rate $r=k/n$ and positive relative distance $\delta=d/n$) will achieve capacity on $BSC$ (binary symmetric channel) if the codes have lower rates than capacity where po …

Supposing Alice and Bob share $\rho$-correlated sequences in $\{0,1\}^n$, what coding theory based schemes are available for Alice and Bod to extract sequences $A,B\in\{0,1\}^n$ respectively such that …

Is there a location where one can access generator matrices (not just bounds) of best known linear codes?

In information theory capacity or best rate achievement techniques are through showing existence if typical sequences of certain measure while in coding theory performance is measured by number of cod …

Denote $P_{2n}$ to be collection of homogeneous total degree $2$ real polynomials in exactly $2n$ variables such that coefficient of every monomial is either $1$ or $-1$. Split variable set into disj …

Given $s,t\in(0,1)$, $c>1$, $n\in\Bbb N$, pick $2^{n^t}$ random vectors $\{v_i\}_{i=1}^{2^{n^t}}$ such that each $v_i\in\{x\in\{0,1\}^{2^n}:|x|_{hamming}={2^{n-n^s}}\}$. If $v_i^\perp$ is projection …

Given $s,t\in(0,1)$, $c>1$, $n\in\Bbb N$, pick ${n^t}$ random vectors $\{v_i\}_{i=1}^{{n^t}}$ such that each $v_i\in\{x\in\{0,1\}^{2^n}:|x|_{hamming}={2^{n-n^s}}\}$. Denote $v_j\cap v_j$ to be vector …

Is the $0$-error capacity of $7$-cycle: $(1)$ known to be of form $7^q$ for some $q\in \mathbb Q$?

There are some natural packing problems that have been asked in mathematics. Some of them are: 1)How many balls can be placed with in a cube? 2)How many equidistant points can be place on the surfac …

Considered the following inner products: $(1)$ $\langle x,y \rangle = \sum_{t=1}^{n}x_{t}y_{t}$ $(2)$ $\langle x,y \rangle_{c} = \sum_{t=1}^{n}x_{t}\bar{y}_{t}$ consider the following surfaces: $\ …

Suppose we have a balanced bipartite planar maximum degree $k$ graph. How many such graphs on $2n$ vertices have at most $f(n)$ maximum number of $4$ cycles for a given function $f:\Bbb R^+\rightarro …

Are there $[n,k]_q$ constant rate $\frac kn$ and constant alphabet linear code families with automorphism group of size $\Omega((n-n^\beta)!)$ that have minimum distance $d=O(n^\alpha)$ and number …

Denote $\mathcal{F_n}$ as collection of multiaffine polynomials $f\in\Bbb F_2[x_1,\dots,x_n]$. Denote total degree of $f\in\mathcal{F_n}$ as $deg(f)$ (note $deg(f)\leq n$). Denote $e_i=(0,\dots,0,\u …

Denote strings $u,v$ from $\{0,1\}^n$. Denote concatenated pair $[uv]$. Denote $$[uv]_{1}=\{[uv]\oplus e_i\}_{i=1}^{2n}$$ collection of pairs with Hamming distance $1$ from $[uv]$ string concatenati …