arXiv subjects

Christophe Mouaha

Publications and source records attributed to Christophe Mouaha.

3 recordsLinked to original sources

arXiv2017

Contraction of Cyclic Codes Over Finite Chain Rings

Let $\texttt{R}$ be a commutative finite chain ring of invariants $(q,s)$ and $Γ(\texttt{R})$ the Teichmüller's set of $\texttt{R}.$ In this paper, the trace representation cyclic $\texttt{R}$-linear codes of length $\ell,$ is presented, when $\texttt{gcd}(\ell, q) = 1.$ We will show that the contractions of some cyclic $\texttt{R}$-linear codes of length $u\ell$ are $γ$-constacyclic $\texttt{R}$-linear codes of length $\ell,$ where $γ\inΓ(\texttt{R})$ and the multiplicative order of is $u.$

cs.IT↗

arXiv2017

On the Lattice of Cyclic Linear Codes Over Finite Chain Rings

Let $\texttt{R}$ be a commutative finite chain ring of invariants $(q,s).$ In this paper, the trace representation of any free cyclic $\texttt{R}$-linear code of length $\ell,$ is presented, via the $q$-cyclotomic cosets modulo $\ell,$ when $\texttt{gcd}(\ell, q) = 1.$ The lattice $\left(\texttt{Cy}(\texttt{R},\ell), +, \cap\right)$ of cyclic $\texttt{R}$-linear codes of length $\ell,$ is investigated. A lower bound on the Hamming distance of cyclic $\texttt{R}$-linear codes of length $\ell,$ is established. When $q$ is even, a family of MDS and self-orthogonal $\texttt{R}$-linear cyclic codes, is constructed.

cs.IT↗

arXiv2015

Non isomorphic pure Galois-Eisenstein rings

Let $n; r; e; s$ be are positive integers and the prime p; the finite local principal ideals ring of parameters $p; n; r; e; s)$ $GR(p^n;r)[x]/(x^e - pu ; x^s),$ is defined by an invertible element u of the Galois ring $GR(p^n; r)$ of characteristic $p^n$ of order $p^{nr}.$ It is called Galois-Eisenstein ring of parameters $(p; n; r; e; s)$. A basic problem, which seems to be very difficult is to determine all non-isomorphism pure Galois-Eisenstein rings of parameters $(p; n; r; e; s).$ In this paper, this isomorphism problem for pure Galois-Eisenstein rings of parameters $(p; n; r; e; s)$ is investigated.

math.RA↗