Toric Codes from Order Polytopes
Mahir Bilen Can, Takayuki Hibi
TL;DR
This paper explores the construction and analysis of toric codes derived from order polytopes associated with specific posets, providing parameter calculations for these codes.
Contribution
It introduces a new class of toric codes based on order polytopes of tree and bipartite posets, with explicit parameter computations.
Findings
Parameters of toric codes from order polytopes are explicitly calculated.
Toric codes from tree and bipartite posets exhibit specific algebraic properties.
The study links combinatorial structures with coding theory applications.
Abstract
In this article we investigate a class of linear error correcting codes in relation with the order polytopes. In particular we consider the order polytopes of tree posets and bipartite posets. We calculate the parameters of the associated toric variety codes.
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Taxonomy
TopicsCoding theory and cryptography · Polynomial and algebraic computation · graph theory and CDMA systems