A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf
.
Toric Codes and Finite Geometries
[article]
2017
arXiv
pre-print
We show how the theory of affine geometries over the ring Z/〈 q - 1〉 can be used to understand the properties of toric and generalized toric codes over F_q. The minimum distance of these codes is strongly tied to the collections of lines in the finite geometry that contain subsets of the exponent vectors of the monomials that are evaluated to produce the standard generator matrix for the code. We argue that this connection is, in fact, even more direct than the connection with the lattice
arXiv:1504.07494v2
fatcat:uhuugt5rzra7pgf42ehag47otq