32 citations · 46 across the 7 of their papers we have counts for
8 papers · 1 filter
Bounds and MacWilliams Identities for codes over Artinian rings
Eduardo Camps-Moreno, Carlos Espinosa-Valdéz, Hiram H. López +2
This work develops new foundations for the theory of linear codes over local Artinian commutative rings. We use algebraic invariants such as the socle, type, length, and minimal nu…
Regularity index of the generalized minimum distance function
Carlos Espinosa-Valdéz, Luis Núñez-Betancourt, Yuriko Pitones
We show that the generalized minimum distance function is non-increasing as the degree varies for reduced standard graded algebras over a field. This allows us to define its regula…
Bounds for the Minimum Distance Function
Luis Núñez-Betancourt, Yuriko Pitones, Rafael H. Villarreal
Let be a homogeneous ideal in a polynomial ring . In this paper, we extend the study of the asymptotic behavior of the minimum distance function of and give bounds…
Unmixed and Cohen--Macaulay weighted oriented König graphs
Yuriko Pitones, Enrique Reyes, Rafael H. Villarreal
Let be a weighted oriented graph, whose underlying graph is , and let be its edge ideal. If has no -, -, or -cycles, or is König, we characterize whe…
Footprint and minimum distance functions
Luis Núñez-Betancourt, Yuriko Pitones, Rafael H. Villarreal
Let be a polynomial ring over a field , with a monomial order , and let be an unmixed graded ideal of . In this paper we study two functions associated to :…
Monomial ideals of weighted oriented graphs
Yuriko Pitones, Enrique Reyes, Jonathan Toledo
Let I=I(D) be the edge ideal of a weighted oriented graph D. We determine the irredundant irreducible decomposition of I. Also, we characterize the associated primes and the unmixe…
Minimum distance functions of complete intersections
Yuriko Pitones, Jose Martinez-Bernal, Rafael H. Villarreal
We study the footprint function, with respect to a monomial order, of complete intersection graded ideals in a polynomial ring with coefficients in a field. For graded ideals of di…
Minimum distance functions of graded ideals and Reed-Muller-type codes
Jose Martinez-Bernal, Yuriko Pitones, Rafael H. Villarreal
We introduce and study the minimum distance function of a graded ideal in a polynomial ring with coefficients in a field, and show that it generalizes the minimum distance of proje…