Results on Binary Linear Codes With Minimum Distance 8 and 10
Iliya Bouyukliev, Erik Jakobsson
TL;DR
This paper classifies binary linear codes with minimum distances 8 and 10 for certain parameters, proves nonexistence for specific cases, and establishes new bounds using advanced algorithms focused on dual codes.
Contribution
It introduces two algorithms for analyzing dual codes and provides new exact bounds for binary linear codes with specific parameters.
Findings
Classification of codes with minimum distance 8 and 10 for certain codimensions
Proof of nonexistence for specific code parameters
Eight new bounds for binary linear codes
Abstract
All codes with minimum distance 8 and codimension up to 14 and all codes with minimum distance 10 and codimension up to 18 are classified. Nonexistence of codes with parameters [33,18,8] and [33,14,10] is proved. This leads to 8 new exact bounds for binary linear codes. Primarily two algorithms considering the dual codes are used, namely extension of dual codes with a proper coordinate, and a fast algorithm for finding a maximum clique in a graph, which is modified to find a maximum set of vectors with the right dependency structure.
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