Affine cartesian codes
Hiram H. Lopez, Carlos Renteria, Rafael H. Villarreal
TL;DR
This paper determines key parameters of affine evaluation codes on cartesian products of finite sets and constructs codes with specific properties, recovering known formulas for minimum distances of various evaluation code families.
Contribution
It provides explicit calculations of dimension, length, and minimum distance for affine evaluation codes on degenerate tori, and constructs codes with prescribed parameters.
Findings
Computed parameters for affine evaluation codes on cartesian products.
Constructed evaluation codes with desired parameters over degenerate tori.
Revealed formulas for minimum distances of various evaluation code families.
Abstract
We compute the basic parameters (dimension, length, minimum distance) of affine evaluation codes defined on a cartesian product of finite sets. Given a sequence of positive integers, we construct an evaluation code, over a degenerate torus, with prescribed parameters. As an application of our results, we recover the formulas for the minimum distance of various families of evaluation codes.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Algorithms and Data Compression