Results on Binary Linear Codes With Minimum Distance 8 and 10

Iliya Bouyukliev; Erik Jakobsson

doi:10.1109/tit.2011.2162264

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arXiv · 1006.0109

Results on Binary Linear Codes With Minimum Distance 8 and 10

Iliya Bouyukliev·Erik Jakobsson

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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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Iliya Bouyukliev, Erik Jakobsson. 2010-06-01. Results on Binary Linear Codes With Minimum Distance 8 and 10. https://doi.org/10.1109/tit.2011.2162264

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