DeepAI AI Chat
Log In Sign Up

On Self-Orthogonality and Self-Duality of Matrix-Product Codes over Commutative Rings

by   Abdulaziz Deajim, et al.

Let R be a commutative ring with identity. The paper studies the problem of self-orthogonality and self-duality matrix-product codes (MPCs) over R. Some methods as well as special matrices are introduced for the construction of such MPCs. A characterization of such codes (in a special case) is also given. Some concrete examples are presented throughout the paper.


page 1

page 2

page 3

page 4


Polyadic cyclic codes over a non-chain ring F_q[u,v]/〈 f(u),g(v), uv-vu〉

Let f(u) and g(v) be any two polynomials of degree k and ℓ respectively ...

LCD Matrix-Product Codes over Commutative Rings

Given a commutative ring R with identity, a matrix A∈ M_s× l(R), and R-l...

Equivalence and Duality of Polycyclic Codes Associated with Trinomials over Finite Fields

In this paper, several conjectures proposed in [2] are studied, involvin...

A Short Note on Self-Duality of Goppa Codes on Elliptic and Hyperelliptic Function Fields

In this note, we investigate Goppa codes which are constructed by means ...

Codes from incidence matrices of hypergraphs

Binary codes are constructed from incidence matrices of hypergraphs. A c...

New perspectives on knockoffs construction

Let Λ be the collection of all probability distributions for (X,X), wher...

Matrix-Product Codes over Commutative Rings and Constructions Arising from (σ,δ)-Codes

A well-known lower bound (over finite fields and some special finite com...