On a Kronecker products sum distance bounds
Armen Grigoryants
TL;DR
This paper investigates the properties of binary linear error correcting codes formed by sums of Kronecker product code families, deriving bounds on their distance and exploring special subclasses.
Contribution
It introduces new bounds on the distance of codes constructed from Kronecker product sums and identifies subclasses with exact distance bounds, unifying some classic code constructions.
Findings
Derived upper and lower bounds for code distance
Identified subclasses with equal lower and upper bounds
Connected classical codes as special cases
Abstract
A binary linear error correcting codes represented by two code families Kronecker products sum are considered. The dimension and distance of new code is investigated. Upper and lower bounds of distance are obtained. Some examples are given. It is shown that some classic constructions are the private cases of considered one. The subclass of codes with equal lower and upper distance bounds is allocated.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Error Correcting Code Techniques