Multivariable codes in principal ideal polynomial quotient rings with applications to additive modular bivariate codes over F4

Producción CientíficaIn this work, we study the structure of multivariable modular codes over finite chain rings when the ambient space is a principal ideal ring. We also provide some applications to additive modular codes over the finite field F4Ministerio de Economía, Industria y Competitividad (MTM2013-45588-C3-1-P / MTM2015-65764-C3-1-P / MTM2015-69138-REDT)Principado de Asturias (GRUPIN14-142

A transform approach to polycyclic and serial codes over rings

Producción CientíficaIn this paper, a transform approach is used for polycyclic and serial codes over finite local rings in the case that the defining polynomials have no multiple roots. This allows us to study them in terms of linear algebra and invariant subspaces as well as understand the duality in terms of the transform domain. We also make a characterization of when two polycyclic ambient spaces are Hamming-isometric.Ministerio de Ciencia, Innovación y Universidades / Agencia Estatal de Investigación / 0.13039/501100011033 (grant PGC2018-096446-B-C21

On the structure of repeated-root polycyclic codes over local rings

Producción CientíficaThis paper provides the Generalized Mattson Solomon polynomial for repeated-root polycyclic codes over local rings that gives an explicit decomposition of them in terms of idempotents. It also states some structural properties of repeated-root polycyclic codes over finite fields in terms of matrix product codes. Both approaches provide a description of the -dual code for a given polycyclic code.MCIN/AEI /10.13039/501100011033 - EU NextGenerationEU/ PRTR (Grant TED2021-130358B-I00)Bulgarian Ministry of Education and Science, Scientific Programme “Enhancing the Research Capacity in Mathematical Sciences (PIKOM)”, No. DO1-67/05.05.2022.TÜB˙ITAK within the scope of 2219 International Post Doctoral Research Fellowship Program with application number 1059B19210116