Equidistant Linear Network Codes with maximal Error-protection from Veronese Varieties

TL;DR

This paper constructs explicit equidistant linear network codes from Veronese varieties, achieving maximal error-protection by ensuring all codewords are equally distant in the vector space metric.

Contribution

It introduces a novel construction of equidistant linear network codes using Veronese varieties, optimizing error correction capabilities.

Findings

Codes have maximal error-protection with equidistant properties.

Explicit construction of vector-spaces with constant dimension.

Parameters of the codes are precisely determined.

Abstract

Linear network coding transmits information in terms of a basis of a vector space and the information is received as a basis of a possible altered vectorspace. Ralf Koetter and Frank R. Kschischang in Coding for errors and erasures in random network coding (IEEE Transactions on Information Theory, vol.54, no.8, pp. 3579-3591,2008) introduced a metric on the set af vector-spaces and showed that a minimal distance decoder for this metric achieves correct decoding if the dimension of the intersection of the transmitted and received vector-space is sufficiently large. From the Veronese varieties we construct explicit families of vector-spaces of constant dimension where any pair of distinct vector-spaces are equidistant in the above metric. The parameters of the resulting linear network codes which have maximal error-protection are determined.