Papers by E. J . García-Claro
arXiv (Cornell University), Feb 20, 2023
Finite semisimple commutative group algebras for which all the minimal ideals are easily computab... more Finite semisimple commutative group algebras for which all the minimal ideals are easily computable dimension (ECD) are characterized, and some sufficient conditions for this to happen are given. A method to build group algebras with this property is presented. Examples illustrating the main results are provided.
arXiv (Cornell University), Feb 21, 2022
If A i is finite alphabet for i = 1, ..., n, the Manhattan distance is defined in n i=1 A i. A gr... more If A i is finite alphabet for i = 1, ..., n, the Manhattan distance is defined in n i=1 A i. A grid code is introduced as a subset of n i=1 A i. Alternative versions of the Hamming and Gilbert-Varshamov bounds are presented for grid codes. If A i is a cyclic group for i = 1, ..., n, some bounds for the minimum Manhattan distance of codes that are cyclic subgroups of n i=1 A i are determined in terms of their minimum Hamming and Lee distances. Examples illustrating the main results are provided.
Journal of Algebra and Its Applications, 2020
Several relations and bounds for the dimension of principal ideals in group algebras are determin... more Several relations and bounds for the dimension of principal ideals in group algebras are determined by analyzing minimal polynomials of regular representations. These results are used in the two last sections. First, in the context of semisimple group algebras, to compute, for any abelian code, an element with Hamming weight equal to its dimension. Finally, to get bounds on the minimum distance of certain MDS group codes. A relation between a class of group codes and MDS codes is presented. Examples illustrating the main results are provided.
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Papers by E. J . García-Claro