

2021ary quasigroups and related topics
September 21, 2018, Novosibirsk, Sobolev Institute of Mathematics, room 135





Equitable partitions and completely regular codes


On the classification of the equitable partitions of the 12cube with the quotient matrix [[0,12],[4,8]]
D. S. Krotov^{} 
Number of views: 
This page:  51 

Abstract:
It is told about the results (j.w. with K.V.Vorob'ev) of computeraimed classification of the equitable partitions the 12cube with the quotient matrix [[0,12],[4,8]], or, equivalently, Boolean functions with a proportion 1/4 of ones achieving the bound on correlation immunity. It is established that there are exactly 16 equivalence classes of such functions; one coloring corresponds to a linear code of dimension 10, two colorings correspond to codes whose linear span coincides with the entire space (that is, codes of full rank, 12), the remaining 13 to codes of 'intermediate' rank 11. An approach is described that makes it possible to obtain the classification.

