Toric surface codes and Minkowski sums

Details Toric surface codes and Minkowski sums Toric surface codes and Minkowski sums

2005-07-28

arxiv.org/abs/math/0507598v2

SIAM Journal on Discrete Mathematics, 20, (2006), 999-1014

Mathematics

Algebraic Geometry

15 pages, 7 figures; This version contains some minor editorial revisions -- to appear SIAM Journal on Discrete Mathematics

Scientific paper

Toric codes are evaluation codes obtained from an integral convex polytope $P \subset \R^n$ and finite field $\F_q$. They are, in a sense, a natural extension of Reed-Solomon codes, and have been studied recently by J. Hansen and D. Joyner. In this paper, we obtain upper and lower bounds on the minimum distance of a toric code constructed from a polygon $P \subset \R^2$ by examining Minkowski sum decompositions of subpolygons of $P$. Our results give a simple and unifying explanation of bounds of Hansen and empirical results of Joyner; they also apply to previously unknown cases.

Affiliated with

Also associated with

No associations

Rating

Toric surface codes and Minkowski sums does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Toric surface codes and Minkowski sums, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Toric surface codes and Minkowski sums will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-562660