Hyperbolic Sets in Incomplete Tables
In this paper, we extend results about the implementation of the Berlekamp-Massey-Sakata algorithm on data tables having a number of unknown values.
cs.IT↗
arXiv subjects
J. J. Simón
Publications and source records attributed to J. J. Simón.
A Note on the Theoretical Support to Compute Dimension in Abelian Codes
In this note we give a theoretical support by means of quotient polynomial rings for the computation formulas of the dimension of abelian codes.
cs.IT↗
Inference of unknown syndrome values in the implementation of the Berlekamp-Massey-Sakata algorithm
We study the problem of finding those missing syndrome values that are needed to implment the Berlekamp-Massey-Sakata algorithm as the Feng-Rao Majority Voting for algebraic geometric codes. We apply our results to solve syndrome correction in abelian codes.
cs.IT↗
From ds-bounds for cyclic codes to true distance for abelian codes
In this paper we develop a technique to extend any bound for the minimum distance of cyclic codes constructed from its defining sets (ds-bounds) to abelian (or multivariate) codes through the notion of $\mathbb{B}$-apparent distance. We use this technique to improve the searching for new bounds for the minimum distance of abelian codes. We also study conditions for an abelian code to verify that its $\mathbb{B}$-apparent distance reaches its (true) minimum distance. Then we construct some tables of such codes as an application
cs.IT↗
Ds-bounds for cyclic codes: new bounds for abelian codes
In this paper we develop a technique to extend any bound for cyclic codes constructed from its defining sets (ds-bounds) to abelian (or multivariate) codes. We use this technique to improve the searching of new bounds for abelian codes.
cs.IT↗
Globalization of twisted partial actions
Let A be a unital ring which is a product of possibly infinitely many indecomposable rings. We establish criteria for the existence of a globalization for a given twisted partial action of a group on A. If the globalization exists, it is unique up to a certain equivalence relation and, moreover, the crossed product corresponding to the twisted partial action is Morita equivalent to that corresponding to its globalization. For arbitrary unital rings the globalization problem is reduced to an extendibility property of the multipliers involved in the twisted partial action.
math.RA↗