منابع مشابه
On tensor products of CSS Codes
CSS codes are in one-to-one correspondance with length 3 chain complexes. The latter are naturally endowed with a tensor product ⊗ which induces a similar operation on the former. We investigate this operation, and in particular its behavior with regard to minimum distances. Given a CSS code C, we give a criterion which provides a lower bound on the minimum distance of C ⊗ D for every CSS code ...
متن کاملRobust Local Testability of Tensor Products of LDPC Codes
Given two binary linear codes R and C, their tensor product R⊗C consists of all matrices with rows in R and columns in C. We analyze the “robustness” of the following test for this code (suggested by Ben-Sasson and Sudan [6]): Pick a random row (or column) and check if the received word is in R (or C). Robustness of the test implies that if a matrix M is far from R ⊗ C, then a significant fract...
متن کاملTotal Perfect Codes in Tensor Products of Graphs
A total perfect code in a graph is a subset of the graph’s vertices with the property that each vertex in the graph is adjacent to exactly one vertex in the subset. We prove that the tensor product of any number of simple graphs has a total perfect code if and only if each factor has a total perfect code.
متن کاملTensor products of ideal codes over Hopf algebras
We study indecomposable codes over the well-known family of Radford Hopf algebras. We use properties of Hopf algebras to show that tensors of ideal codes are ideal codes, extending the corresponding result given in [4] and showing that in this case, semisimplicity is lost.
متن کاملTensor Products of Weakly Smooth Codes Are Robust
We continue the study of robustly testable tensor codes and expand the class of base codes that can be used as a starting point for the construction of locally testable codes via robustly testable tensor products. In particular, we show that all unique-neighbor expander codes and all locally correctable codes, when tensored with any other good-distance code, are robustly testable and hence can ...
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ژورنال
عنوان ژورنال: Annales de l’Institut Henri Poincaré D
سال: 2019
ISSN: 2308-5827
DOI: 10.4171/aihpd/71