7 papers · 1 filter
Duality on group algebras over finite chain rings: applications to additive group codes
Maryam Bajalan, Javier de la Cruz, Alexandre Fotue Tabue +1
Given a finite group and an extension of finite chain rings , one can consider the group rings and . The group ring …
Trace duality and additive complementary pairs of additive cyclic codes over finite chain rings
Sanjit Bhowmick, Kuntal Deka, Alexandre Fotue Tabue +1
This paper investigates the algebraic structure of additive complementary pairs of cyclic codes over a finite commutative ring. We demonstrate that for every additive complementary…
On polycyclic linear and additive codes associated to a trinomial over a finite chain ring
Abdelghaffar Chibloun, Hassan Ou-azzou, Edgar Martínez-Moro +1
In this paper, we investigate polycyclic codes associated with a trinomial of arbitrary degree over a finite chain ring We extend the concepts of -isometry and …
Galois hulls of constacyclic codes over affine algebra rings
Indibar Debnath, Habibul Islam, Edgar Martínez-Moro +1
Let the affine algebra given by the ring , where is the ideal …
On general self-orthogonal matrix-product codes associated with Toeplitz matrices
Yang Li, Shixin Zhu, Edgar Martínez-Moro
In this paper, we present four constructions of {general} self-orthogonal matrix-product codes associated with Toeplitz matrices. The first one relies on the {dual} of a known {gen…
-polycyclic codes in Ore extensions over rings
Maryam Bajalan, Ivan Landjev, Edgar Martínez-Moro +1
In this paper, we study the algebraic structure of -polycyclic codes, defined as submodules in the quotient module , where is the Ore extension ring, $f\i…
On -MDS codes and a conjecture on infinite families of -MDS codes
Yang Li, Shixin Zhu, Edgar Martínez-Moro
The class of -maximum distance separable (-MDS) codes {is a} generalization of maximum distance separable (MDS) codes {that} has attracted a lot of attention due to its…