Results on Binary Linear Codes With Minimum Distance 8 and 10

All linear binary 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 a...

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Veröffentlicht in:	IEEE transactions on information theory 2011-09, Vol.57 (9), p.6089-6093
Hauptverfasser:	Bouyukliev, I. G., Jacobsson, E.
Format:	Artikel
Sprache:	eng
Schlagworte:	Algorithms Applied sciences Binary codes Binary system classification of codes Coding theory Coding, codes Computer and Information Science Data- och informationsvetenskap Exact sciences and technology Generators Information theory Information, signal and communications theory length Linear code Linear codes optimal codes Parity check codes Signal and communications theory Telecommunications and information theory Vectors
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Beschreibung
Zusammenfassung:	All linear binary 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.
ISSN:	0018-9448 1557-9654 1557-9654
DOI:	10.1109/TIT.2011.2162264