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Towers of Betti Numbers of Matroids and Weight Distribution of Linear Codes and their Duals
(Master thesis; Mastergradsoppgave, 2015-05-15)
The main notion behind the study of matroids is linear dependence. In this thesis, we give a survey of the concepts and properties of linear error-correcting codes over finite fields being dependent only on the matroids derived from these codes. In particular, the weight distributions of linear codes, and their extensions, over bigger fields are only dependent on the N-graded Betti numbers of these ...