Related papers: Recursive Structure of Hulls of PRM Codes

We study one generator quasi-cyclic codes and four-circulant codes, which are also quasi-cyclic but have two generators. We state the hull dimensions for both classes of codes in terms of the polynomials in their generating elements. We…

Frameproof codes are used to preserve the security in the context of coalition when fingerprinting digital data. Let $M_{c,l}(q)$ be the largest cardinality of a $q$-ary $c$-frameproof code of length $l$ and $R_{c,l}=\lim_{q\rightarrow…

We introduce an algebra of elliptic commuting variables involving a base $q$, nome $p$, and $2r$ noncommuting variables. This algebra, which for $r=1$ reduces to an algebra considered earlier by the author, is an elliptic extension of the…

In this paper we derive strong linear inequalities for sets of the form {(x, q) \in Rd \times R : q \geq Q(x), x \in Rd - int(P)}, where Q(x) : Rd \rightarrow R is a quadratic function, P \subset Rd and "int" denotes interior. Of particular…

Given integers $a$ and $m\ge 2$, let $\Hm$ be the following set of integral points $$ \Hm= \{(x,y) \ : \ xy \equiv a \pmod m,\ 1\le x,y \le m-1\} $$ We improve several previously known upper bounds on $v_a(m)$, the number of vertices of the…

We prove a structure theorem for multiplicative functions which states that an arbitrary bounded multiplicative function can be decomposed into two terms, one that is approximately periodic and another that has small Gowers uniformity norm…

Let R be a commutative ring, q a unit of R and P a multiplicatively antisymmetric matrix with coefficients which are integers powers of q. Denote by SE(q,P) the multiparameter quantum matrix bialgebra associated to q and P.Slightly…

A framework of monomial codes is considered, which includes linear codes generated by the evaluation of certain monomials. Polar and Reed-Muller codes are the two best-known representatives of such codes and can be considered as two extreme…

Finite dimensional irreducible modules of the two-parameter quantum enveloping algebra $U_{r,s}(\mathfrak{sl}_n)$ are explicitly constructed using the fusion procedure when $rs^{-1}$ is generic. This provides an alternative and…

A Theorem of V.Ovsienko characterizes sequences of positive integers $(a_1,a_2,\ldots,a_n)$ such that the $(2\times2)$-matrix $\begin{pmatrix} a_n & -1 \\ 1 & 0 \end{pmatrix}\cdots \begin{pmatrix} a_1 & -1 \\ 1 & 0 \end{pmatrix}$ is equal…

The particle representation model (PRM) and interacting particle representation model (IPRM) describe homogeneous turbulence through orientation-conditioned structural states. In their original form, the conditional state is organized by…

A rational projective plane ($\mathbb{QP}^2$) is a simply connected, smooth, closed manifold $M$ such that $H^*(M;\mathbb{Q}) \cong \mathbb{Q}[\alpha]/\langle \alpha^3 \rangle$. An open problem is to classify the dimensions at which such a…

The partition statistic $V_R$-rank is introduced to give combinatorial proofs of the Ramanujan type congruences mod 3 for certain classes of partition functions.

Consider the Hales-Jewett theorem. The $k$-dimensional version of it tells us that the combinatorial space $\mathcal{U}_{M, \Lambda} = \{ \eta \mid \eta: M \to \Lambda \}$ has, under suitable assumptions, monochromatic $k$-dimensional…

A multifiltration is a functor indexed by $\mathbb{N}^r$ that maps any morphism to a monomorphism. The goal of this paper is to describe in an explicit and combinatorial way the natural $\mathbb{N}^r$-graded $R[x_1,\ldots, x_r]$-module…

The (n,k)-hypersimplex is the convex hull of all 0/1-vectors of length n with coordinate sum k. We explicitly determine the extension complexity of all hypersimplices as well as of certain classes of combinatorial hypersimplices. To that…

Let F* be the finite field of q elements and let P(n,q) be the projective space of dimension n-1 over F*. We construct a family H^{n}_{k,i} of combinatorial homology modules associated to P(n,q) over a coefficient field F field of…

The paper deals with the problem of deciding if two finite-dimensional linear subspaces over an arbitrary field are identical up to a permutation of the coordinates. This problem is referred to as the permutation code equivalence. We show…

We compute the Gromov-Witten invariants of the projective plane blown up in r general points. These are determined by associativity from r+1 intial values. Applications are given to the enumeration of rational plane curves with prescribed…

We construct QCD sum rules for nonperturbative studies without assuming the quark-hadron duality for the spectral density at low energy on the hadron side. Instead, both resonance and continuum contributions to the spectral density are…